One question for you both . Where was the Holy Spirit when the resurrecting was taking place ?
Honesty is the best policy, in truth. The Holy Spirit was doing the heavy-lifting...it was the Fathers' own (Holy Spirit). It is a part of him, of the same one person. The Holy Spirit is not another Spirit person that is truly holy, besides the Father's Spirit.
Here's one rendition of how it all went down:
Jesus, the mortal man, died on the Cross to gain his salvation to new life. His human spirit separated from his human body as Jesus cried out to his Father - Jesus was now dead, and did not exist at the moment in time, at least of no energy or life.
Then after 3 days, as promised by his Father: A 'portion' of his Father's spirit became 'fused' into Jesus' spirit, in the keep of his Father. This ignited and caused new life, new life of immortality into Jesus, placed also into his body, that was now altered to accommodate this new immortal life.
Per scripture: Jesus became the first from the dead risen into immortal life, and many would follow him. Jesus was born as the natural born believer in God as his God dwelt in him, his Spirit. And at his death, he gained his own salvation, the glory he was praying for since the foundation of the world as the plan and promise of his God. He is the example and the process of life for every believer from rebirth to immortality.