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

Creative tools and rule bending

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

Offense

+5 AD or 9 AP
Flex

+5 AD or 9 AP
Defense

+8 Magic Resist

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.