Arcana Coelestia # 535
535. The Church called Noah must not be reckoned among the Churches that came before the Flood. This becomes clear from verse 29, which says that that Church 'would comfort them from their work and from the toil of their hands that came from the ground which Jehovah had cursed'. The comfort was that it would live on and endure. Noah and his sons however will in the Lord's Divine mercy be dealt with later on.
Three
The number three in the Bible represents completeness. That's why Jesus rose on the third day after the Crucifixion -- his transformation was complete. It's why Elijah stretched himself on the dead child three times, why Jonah was in the belly of the fish for three days, why the Lord called Samuel three times, and many more. It's also reflected in the fact that there are three levels of heaven, three levels of hell, three levels to human life and, ultimately, three aspects of the Lord Himself: Father, Son and Holy Spirit.