Active and Passive LTM pairs. Moving between prod1 and prod2

For the prod1 and prod2 parts, there are multiple ways to do that. I would just setup 2 virtual servers and 2 pools. One virtual server is production, and the other test. One pool represents prod1, and the other prod2. When they want to switch environments, just point production virtual server to pool prod2. Only new connections will be affected, so new connections will start to go to pool prod2.

Can you explain the number of HA pairs you will use? Also, what function they will have, as I can't understand why you need 3 pairs.