There's only one Heaven in the sense the heavenly dimension, but it is manifested differently according to God's Timetable.
The different 'planes' in Heaven idea actually comes from pagan religion, including Jewish mysticism of the Kabbalah.
This is a common mistake. Christianity has become so secularized that most believers are unaware of the subtle nuances of the faith.
The Bible states that there are three heavens. More to the point, it actually describes what goes on at each level.
Let's start with the actual numerical count, given by St. Paul.
I know a man in Christ, fourteen years ago (whether in the body, I know not; or whether out of the body, I know not; God knoweth), such a one caught up even to the third heaven.
2Co 12:2
The above passage is acknowledged by most scholars to be a testimony of St. Paul even though he phrased it as though it was an acquaintance. Note the last two words "third heaven". The number three implies at least two more; #1 & #2. Since Paul declares that #3 is the highest, it is logical and safe for us to assume that #1 is the lowest.
The Old Testament provides an actual physical layout or template of the construction of the heavenlies along with the first description of what goes on there.
Beginning in Exodus 25:9 we have the divine command to Moses to construct the tabernacle. In the 26th chapter of the same book we read the commands of how it is to be fitted out replete with measurements, colors and types of construction material. It all continues in Exodus 35, 36 and so on. Later on, the temple is constructed in the days of King Solomon. Although it's a building of stone and wood instead of cloth and wood, the temple design is identical. The temple was later wrecked and rebuilt in the days of Herod. Jesus walked in it and the N.T. has many passages that refer to it - as well as something wonderful that happened there on the day Christ died.
The basic design is this:
An outer wall either of curtain or stone that separates the world at large from the court.
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Only members of the Hebrew people were admitted into the court the curtains and/or walls created.
There was a separation INSIDE the court which created yet another -inner- room or area. This area was called the Holy of Holies.
The Ark of the Covenant was placed in this inner room. Only the high priest was allowed in there to offer sacrifice to God on behalf of the people AND THEN ONLY ONCE A YEAR. The man wore a special garment and had a rope tied around his waist. In the event God should kill him there, helpers on the outside could drag his dead body out without entering. The robe also had tiny bells sewn into it. The outside helpers listened intently for silence, which suggested something bad had happened to the priest.
There was a veil or cloth curtain hung in the doorway of the Holy of Holies. It signified a separation or barrier between the inner room/Holy of Holies and the outer court.
The pattern was repeated in the second temple, except that somewhere along the way the Ark of the Covenant disappeared. Indiana Jones knows where it is.
THE MEANING of the pattern provides the template of the three heavens.
The outer curtain separated the whole world from the courtyard where only God's people could enter.
That which was outside the curtain is the first heaven - the physical world we live in.
That which was inside the curtain where only God's people could go is the second heaven.
That which was inside the Holy of Holies where only the high priest could go is the third heaven.
On the day Jesus died, the veil in the second temple was ripped in two, thus signifying to all that those who were in the court or second heaven would have access to the Holy of Holies - or the high throne of God. No priest was needed any longer because the sacrifice of Christ had been accepted by He who dwells within.
On this point alone rests the significance of the Christian's right to enjoy personal access to the Almighty.
THIS is the meaning of all the explanation of the numbers of the heavens.
Note that people who live in the outside world are denied access to both the court and to the Holy of Holies.
They must become God's people by adoption first.*
THREE HEAVENS, see?
The scripture is so explicit and the notion is so pervasive throughout the Bible that this design cannot be construed as having been taken out of context. It and references to it are repeated over and over. It is a revelation from God of the construction of the heavens.
The Qur'an says there are seven heavens, but the book provides nothing that comes close to the detail of description contained in the Bible. I know, I've looked.
Secular society provides a lot of stories, but they are simply that - fiction.
Most secular people have no real idea what Jesus did on the cross either.
Pity.
Hope this helps. I invite study on this matter as I've found it fascinating stuff. I'm sure I've missed a point or two, but my primary goal here is to establish without doubt that there are indeed three heavens.
Hint: what mischief goes on in #2? Some scholars suggest that the throne of the evil one is there (since he was tossed out of the inner area). Satan and it's demonic host have also been 'grounded' in the modern sense that they cannot fly as Holy angels do in the first heaven (#1). Did you know that? In any case, a lot of things go on there that the uninitiated THINK is heaven, near death experiences for example.
Hope this helps.
* There are obscure passages which refer to "trespassers". Does this suggest that some 'outside' people occasionally sneak through the wall into the court? These passages also suggest that 'treaspassers' are ejected summarily. That is a matter for further study.