Scriptures speaks more clearly about 7 spirits than about 7 heavens.
The 7 spirits of God are mentioned in Revelation [Rev 1:4, Rev 3:1, Rev 4:5, Rev 5:6] and perhaps identified in Isaiah 11:2 as:
1) the Spirit of the Lord,
2) the Spirit of wisdom,
3) the Spirit of understanding,
4) the Spirit of counsel,
5) the Spirit of might,
6) the Spirit of knowledge, and
7) the fear of the Lord
As to heavens, consider the following verse:
"And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven." John 3:13
Jesus was seemingly speaking of more than one heaven. The one He came down from would have been the 3rd heaven where He was before His natural birth in Bethlehem. Yet, while here among us Jesus was also still in heaven, this is a heaven where we can also be, is it not?
Consider the following:
The ark of Noah had three levels and the creatures on all three levels were saved from the flood waters. The unclean beasts were on the bottom. The clean beasts were on the 2nd level and Noah along with 7 members of his family were on the top. Some of all three types were “saved” from the destruction of the flood.
The Israelites were not allowed to eat of "unclean beasts" at all because the cost of eating them was greater than the cost of going hungry. In other words, the net value of eating them was NOTHING or less than nothing. [Their words and actions produce no good fruit, but evil fruit only.] All the fruits of an unclean beast are filthy rags and good for nothing in the eyes of God.
But it is when we were as beasts that were not clean that most of us first were drawn to God. We were “saved”, but until He worked on us we remained unclean.
First heaven, if you will, would be the lowest level at which God deals with man. It would correspond to the lowest level of the Ark built by Noah.
The natural children of Israel in the wilderness wandered back and forth between their own ways of confusion and God’s Way of order. They were continuously in need of repentance and God’s mercy even though He had saved all of them from slavery in Egypt. Most of them in the end did not make it into the promised land. Only two adults [above the age of 20…see Numbers 32:11-12] who came out of Egypt also made it into the promised land: Joshua and Caleb. Instead of going back to the tabernacle with the proper sacrifice, most of the people went to golden calves; or the gods of the heathen people in the lands; or they looked back with longing to Egypt [their own vomit - II Peter 2:22].
Similarly, today we are too often like yo-yo’s bouncing back and forth between God’s Way and our own ways.
We have heard it said that “we are what we eat” in reference to the consumption of natural foods. When we first are drawn from the depths of sin we are like those unclean beasts because of what have been eating spiritually. We need to have our filth cleaned out [Matt 12:43-44] and we need to eat of His 12 fruits [Rev 22:2] and His 7 spirits [Rev 3:1, Rev 5:6, Isa. 11:2]. The unclean beast of man [Eccl 3:18-21] continues to eat spiritual garbage until (and if) it learns the difference between good and evil food and drink and nourishes itself properly [John 6:35]. If it eats garbage after being cleansed it will again become filthy once again [Matt 12:45] only worse.
Second heaven is where God continues to deal with man's beastly nature through the gift of His Spirit and would correspond to the second or middle level of the Ark which Noah built. Men who enter here have been cleaned up and thus are 'clean beasts', but still beasts since their “old man” [Eph 4:22-23] is still seeking the dominion.
When the filth, which is a part of us is being removed and as we are beginning to serve Him (eating & drinking properly) then His fruits [partial listing in Gal 5:22-23] will begin to grow in us. Then will we be able to provide the proper nourishment of the things of God to others as well. Yet, the lust of the eyes and the lust of the flesh and the pride of life [I John 2:16] still assail us. As we continue to partake of the evil food and drink, in any measure, so also in that measure the fruit, which we bear is still our own [Gal 5:19-21]and is thus poisonous to God's people.
When we are “clean beasts" our evil fruits have been removed, but our beastly nature, which is drawn to sin remains. “Clean beasts” have a mixture of edible and inedible parts. The Israelites were not allowed to eat all of every single part of even clean beasts [Lev 3:4 & 17]. This is why when we read a writing (such this one) or hear a preacher preach we need to sift through it carefully so as not eat unnecessarily any poisonous thing. But if we do at times, we must remember also these words: “…and if they drink any deadly thing, it shall not hurt them…” Mark 16:18
"Wisdom hath builded her house, she hath hewn out her seven pillars:” Prov 9:1 [Would these pillars not be the 7 Spirits of God?]
“She hath KILLED her beasts; she hath mingled her wine; she hath also furnished her table." Prov 9:2 [She killed the source of evil within us which are the remains of our “old man”, the “unclean beast” . She mixed the Word of God with the Spirit of God to bring it to Life in us. She put before us a table of nourishing food and drink (the Word and the Spirit).
Third heaven corresponds to the highest level of the Ark which Noah built. The beastly natures of men must be dead in order to enter here. No sin and no ways of man are allowed within.
When all of the fruits of our beast are gone and our beast nature itself is gone then and only then will we be ready to enter the 3rd heaven where the Father dwells (as He dwelt in the most holy place between the cherubims [II Sam 6:2]in the tabernacle in the wilderness. Before that our filthy inner parts and our filthy outer parts would cause us to be consumed by the consuming fire which God is...if we were to approach His throne...
The three levels or heavens are pictured then in the three levels of Ark of Noah but also in the three levels of the tabernacle in the wilderness.
The veil to the most holy place or the holiest of holies was rent when Jesus died [Matt 27:50-51], but we still cannot enter in there without being properly cleansed [Acts 2:38] and attired [Matt 22:11-13, Eph 6:14-17].
Everyone that comes to Christ can enter the 1st level [outer court] of the tabernacle (in order to repent and receive and be received of Him), but only priests with the proper garments [Exodus 28] can enter the 2nd level [holy place]. Prior to sacrifice of Jesus no one could enter the real 3rd level [most holy place or holiest of holies] and live.
The natural high priest once a year entered the most holy place (3rd level) a shadow 3rd heaven in the tabernacle in the wilderness. Even Moses was not to actually able enter in where he would have been able to look on the face of God [Ex. 33:20].
Jesus is the Way in... but obviously, to me anyway, not everyone who comes to Him is immediately ready for third heaven.