[quote=TheEvanCat]
I doubt that Azerbaijan would agree to be "annexed" annexed by Turkey. They're allies, but they're very distinct countries. I believe that it would probably just be a close-knit alliance.And then if the Turks try anything Iran is there to back up Armenia. Mostly because they have a large minority in Iran and there's a lot of interdependence with trade and culture and stuff.
[/quote]

I believe that annexation of Azerbaijan could be possible because they both have went through a world war. Azerbaijan may have been attacked by northern forces i.e the great and powerful Russia who managed to conquer Georgia and Armenia. Azerbaijan would have been crushed by these forces and lost some land during the process.

Turkey has similarly lost and gained some land (losing the Thracian part of Turkey but gaining Cyprus) to Greece, but they may have suffered less compared to Azerbaijan, which is much smaller and may have been weakened.

The problem I see with annexing Azerbaijan is possibly angering Kemalist nationalists, and creating some issues with Georgia, Iran, Turkmenistan, and the other "Turkic" states. Russia and Iran might react negatively, especially Iran for possibly instigating an Azeri uprising (Iran has a big Azeri population). 

Turkey might benefit overall, since Azerbaijan links to the Caspian Sea and most of all, natural resources that Turkey lacks.