1: Consider getting rod of the ages earlier, as you want to have it at least 10 minutes for full power. Most games wont last until youve gotten boots, rylais, rabadons and then 10 minutes after you get rod of the ages.

2: Dont put a mastery point in improved flash if you don't use it :)

3: If you have mana problems, consider getting seals of clarity instead of ap. The deathcaps and the staffs give enough ability power. Annie doesnt rly need the ap early game, she can still 1-shot any1 at lvl 6 . If you cant afford mana runes, just try to pick up an early tear of the godess and you will be fine

4: You want to have flash with annie. She is very slow and most of the time you are very predictable. If you move forward to use utli, the enemy will back away. But then, u flash in and pull all cds without giving them any time to react. You may build her tankier than most do, but that doesnt mean that she will last more than one second if she stands in the middle of a teamfight.

These are only my opinions, nothing that you have to follow if you dont want to.
I'm not sure if i like this build or not yet, so I won't vote.