To address the issue of state-by-state certification, there are, in fact, 3 states that do NOT require you to be certified according to the AANA. Those states are: Michigan, Indiana, and Hawaii. However, even though certification may not be required, I'm sure it would be harder to get hired as an uncertified anesthetist -- I don't know how comfortable potential employers would feel about bringing on someone without specialty certification.
This information can be found by searching "certification" on the AANA website.
A PDF of the certification requirements is the 3rd entry that comes up on the list when you search "certification."