Anivia is mighty scary to face as anyone, if your unable to dodge her short bur- oh the other way around.
Yeah pretty much what the other posts said.
Despite being the best tower diver in the game, he still wont be able to kill you if you're egged next to your tower, alone anyways. Your burst combo can be done outside transfusions range, try your best to harass him, he wont or shouldn't be bothering you with half health. As long as you position your self smart and out farm him (rather hard, he farms waaaaay too easy), you should be good.
As Vladimir, Anivia is the only solo mid character I've had trouble vs (well, and udyr mid with smite and all mr runes.) Last game, I've gotten first blood off her, but she carried the match immediately after as she ganked repeatably though I called mia and pinged each time :\.