Anivia

Middle

Bird is the Word

Massive scaling damage and Zhonya's safety.

Sorcery

Empowered abilities and resource manipulation

Arcane Comet

Hitting a champion with spells hurls a comet that deals adaptive damage at them. Landing more spells reduces Arcane Comet's cooldown.
Manaflow Band

Hitting enemy champions with a spell grants maximum mana.

After reaching 250 mana, Manaflow Band restores 1% of your missing mana every 5 seconds.
Transcendence

Gain 10% CDR when you reach level 10. Excess CDR becomes AP or AD, Adaptive.
Gathering Storm

Gain increasing amounts of AD or AP, Adaptive over the course of the game.

Inspiration

+20 Ability Power or +12 Attack Damage, Adaptive

Perfect Timing

Gain a free stopwatch. Stopwatch has a one time use Stasis active.
Cosmic Insight

+5% CDR
+5% Max CDR
+5% Summoner Spell CDR
+5% Item CDR

WhyArcane Comet

Anivia's damage almost always comes with a stun or slow, allowing for a much more reliable hit rate on Arcane Comet.

She is also able to reduce the cooldown of Comet quite quickly with [E] and [R].

WhyManaflow Band

Manaflow Band is a great rune on mid laners who stack multiple mana items (Tear, RoA etc.), providing even more mana return.

WhyTranscendence

Typical choice here for mid mages. CDR is always a great stat for trading and doing more damage.

WhyGathering Storm

Anivia is a champion who can very easily stall the game thanks to her [R] waveclear, and thus she can get some insane AP from forcing a stalled-out game.

WhyPerfect Timing

Perfect Timing allows you to get a cheaper Zhonya's after Archangel's + RoA giving you a massive mid-game.

With Cosmic Insight your Zhonya's cooldown will be down to 96s.

WhyCosmic Insight

Cosmic Insight provides a lot of defensive power in the form of Summoner Cooldown and Item Cooldown for Zhonya's/Archangel's.

If you'd prefer to accelerate your mid game item power-spike you can also take Magical Footwear here.