Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This is my AP/Tank hybrid build for Anivia that will end up with about 3000hp+ and 700ap+ and thanks to masteries and neutral golem buff 29-34% reduced cooldowns.
Anivia wants tons of HP, MP, and AP and there happend to be an item that provides all three in excess: Rod of Ages, so get two of them as early you can.
I tend to vary the rest of the item build a lot, like the boots for instance: if its going well, set it in stone with Sorc's, and if its going poorly maybe get boots of swiftness or mobility instaid to run out of ganks and save time after dying (this Anivia will be running back and forth to the jungle a lot so it helps).
I like to use Clarity over Ignite as a summoner spell because Ignite will just force you to get in THEIR range, this build focuses on Flash Frost over Frostbite so thats not needed, try to stay out of their range to exploit the harrassing potential of Flash Frost (if you got aim) before you get in their range and finish them of with Glacial Storm + Flash Frost + Frostbite combo and later + Lichbane auto attack.
Get Glacial Storm as quickly you can at level 6 and then level 15 and 16 after 3 levels of Crystallize because you can do with just 3 levels in Crystallize til later.
Early Game: Go mid with a Ruby Crystal and start creeping with your Flash Frost at the same time you harrass the opposing champion until you reach level 6-11 then you recall you get a potion at base if your level 6-7 but if your higher you wont need one.
Now go to the golem and get the golem buff by killing it, with this you are ready to gank and maybe get a kill or two in mid if not that at least a tower or lane control.
Mid Game: When you got your Mejai's Soulstealer and maybe the second Rod of Ages you should be ganking with your team-mates if it goes well the game is won with early 250ap+ they will take a **** load of hurts.
Dont forget the Golem buff you want it at almost ALL TIMES period.
So if you see your golem buff is about to go out (1/4 left or so before it expires) i would go to the other golem buff and grab it but this build can make it a pain against warwicks (or with warwicks in your team) because they tend to steal your buffs.
End Game: By now you are either OK or Ownage if its going well getting a Zhonya's Ring will really buff up your damage potential to new heights, the are likely to surrender if you get it, but if its going poorly a well coordinated defense will be neccissary and you WILL need golem buff for defense with one to three inhibs down.