Massive scaling damage and Zhonya's safety.
Empowered abilities and resource manipulation
Hitting a champion with spells hurls a comet that deals adaptive damage at them. Landing more spells reduces Arcane Comet's cooldown.
Periodically your next ability used has its mana or energy cost refunded and restores some of your missing mana or energy.
Gain 10% CDR when you reach level 10. Excess CDR becomes AP or AD, Adaptive.
Gain increasing amounts of AD or AP, Adaptive over the course of the game.
+20 Ability Power or +12 Attack Damage, Adaptive
Gain a free stopwatch. Stopwatch has a one time use Stasis active.
+5% Max CDR
+5% Summoner Spell CDR
+5% Item CDR
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].
Manaflow Band is a great rune on mid laners who stack multiple mana items (Tear, RoA etc.), providing even more mana return.
Typical choice here for mid mages. CDR is always a great stat for trading and doing more damage.
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.
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.
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.