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.
Just one of the builds i use. Ghost is useful as anivia is slow, good for getting into good position to flash frost or rush ahead and plant a wall. Teleport is useful because your slow and helps you get to teammates fast and aid them. You can also use teleport right before you turn into an egg to teleport your egg. The same trick can be used with guardian angel. GA>Egg since you can be stunned in your egg.
Masteries are the usual mage set up i would think, not much to explain there.
As for item build i take tear of goddess first. To be honest i sometimes rush rod of ages instead, but i find it takes longer to reach 1000 mana than it is to reach 10 mins after building rod of ages. You'll need this mass mana pool to benefit from archangels staff. I take mejal's because as anivia you should be rarely dying and be getting lots of kills/assists. Even if its not a good game for you youll eventually get the 180ap of 20 stacks or at least 13 stacks. The rest of the items are pretty self explanatory. More ap, more penetration. End game sell your soul stealer for another archangels.
For the skills i get flash frost first as it is the best for killing waves of creeps. just hit with both ends of flash frost and it decimates enemies.