Anivia build that really focuses on heavy damage with her ult and using her wall strategically both offensively and defensively.

The Grail and the Seraph's are heavy mana regen items that allow you to span her ult constantly.
Her ult should be used a lot both offensively and defensively so you need to make sure you always have mana and you dont want to have to rely on the blue buff.

The Torment is your strongest weapon against tanks and works perfectly alongside her ult. This should be the first item finished because it is the most damaging item early game when she does almost nothing to other champions with her ult.

The Will of the Ancients works well with her ult, even if it's not as noticeable because her ult is a toggle.
This allows her to sustain health early game, provide an aura support for team fights, and makes it so that she can just farm at late game to restore health that might have been lost during a team fight or after she revives from an egg.

The boots of swiftness help make up for her extremely slow movement speed. Her biggest weakness is getting caught by ganks and not being able to get away even after putting up her wall. This item makes up for that.

Anivia should always be behind all other champions along with the ADC. She is extremely squishy and even with health items she dies very quickly. During team fights, your ult should be up to constantly damage and slow the other team and your wall should be used to divide the opposing team so that your team can quickly pick off champions. The Flash frost should be aimed at the ADC to prevent them from dealing the large amounts of damage they do. Your ult should help considerably against tanks because of the Torment and so while you all focus whomever you decide, you will still be taking the tank out as well.