Hmm... Arcane Helix...
That may be fun for blue-reliant mages... and yet ANOTHER recipe Anivia can do silly things with that requires a catalyst. (Oh you're sieging this tower? I'll just put this ult down to stop you and CRAZY HEAL)
New Avarice Blade: OH GOD THE BANKPLANK
Boots of Speed: Now has kinda-tenacity... that... changes my Anivia build
DFG: You fools! You've unleashed the madness of AP Rengar again!
Frozen Fist: Oh man, that's going to be fun on Zyra
Ohmwrecker: Oh god the diving
Warmog's: RIP old Warmog's
Zephyr: There's your AD Cooldown item