um just a few things. I am not sure why you started off with Amplflying Tome. The only you get out of it is 10 AP. If you want AP why not get a Doran's Ring which gives you AP, Manga Regen and 100 HP. Everything you need early game in one. Alternatively you could go Sapphire Crystal and two Health Potion to have a bigger mana pool and some health regen when you need it.

Regarding cheat sheet 1 Abyssal Mask does not stack with another. As it is Uniqie Aura meaning only one works. The 2.7k gold spent on it could be used elsewhere e.g. A portion of your Rabadon's Deathcap.

Regarding cheat sheet 2, 2 Rod of Ages isn't that good. You could get something like say Rylai's Crystal Scepter for just a few extra gold or start building your Rabadon's Deathcap.

Now in general regarding items. Hextech Gunblade isn't good on Anivia as her normal attack is really bad. You are probably better off with say a Will of the Ancients if you are planning to upgrade your Hextech Revolver. I am quite surprised you don't have a Rabadon's Deathcap it is a core item in AP heroes. Anivia has horrendous movement speed. Funny she is a bird yet she is so slow. Getting your boots so late is a really bad idea! You should get your boots asap or earlier in the game.

I highly recommend maxing Frostbite by level 9 as it is your main source of damage. Flash Frost is hard to aim and the stun does not increase with each level so definately maxing Frostbite asap is the way to go.