Heaven" and "heavens" are used many times in the Bible, with a couple of variations of meaning. Sometimes it is relatively literal, including times when the Lord is identified with it (“Our Father, who art in the heavens,” for instance), meaning heaven as the eternal home for people who chose to do what is good in this life and let the Lord lead them to a love of being good. In other references, particularly when it is paired with “earth” or other lesser ideas (“In the beginning God created the heavens and the earth,” for instance), “heaven” or “heavens” means our internal life as opposed to our external life. In a way, these two meanings are really the same. If you think about the importance of your deepest thoughts and feelings, you can see that they are the “real” you, much more so than your body is. The relationship between the spiritual world and the natural world is similar; the spiritual world is the “real” one, and controls the natural world the same way our thoughts and feeling control our actions. So in both cases, “heaven” describes a deeper reality that we will enter fully after we die.

'The spirit of God,' as in Genesis 1:2, signifies the divine mercy of the Lord.

'The spirit of God' denotes good from an interior level, so from the divine. The spirit of God is what proceeds from the divine, so from good itself, because the divine is good itself, and what proceeds from it is truth within which is good. This is what 'the spirit of God' signifies in the Word, because the spirit itself does not proceed, but the truth itself within which is good, the spirit being the instrument which produces it.

(References: Arcana Coelestia 19; Divine Love and Wisdom 100)