Why do you like them? I'm legitimately curious, because compared to pretty much any other mage in the game, Anivia has the most trouble farming, despite being incredibly gold-reliant in order to get her RoA and Seraph's as quickly as possible.
Now, I can understand having bad basic attacks as a weakness. Anivia's a burst mage who specializes in area control, and has rather high damage, fantastic CC, a really good wall, and a revival passive. All this on top of one of the best waveclears in the game, as long as she has enough mana and AP to use it as such.
The problem, then, lies in farming without her ultimate, which is what you'll want to focus on pre-6 anyway. Anivia has incredibly low AD, low enough that farming under her turret is a massive pain. Combined with a low attack speed and moderate projectile speed, and it becomes really easy to whiff the minion. And with slow attack frames, you have to stand (hover?) in a potentially bad spot for noticeably longer than most midlaners to get the attack off, the frustration of which is compounded by her attack sound playing before the crystal launches--the same problem that Quinn and Garen have received complaints about in the past.
I mean, even Karthus got his abysmal attack frames buffed at some point after his VU, despite that he can easily just farm with Lay Waste, and possibly harass the enemy in the process. Why does Anivia deserve such an awkward attack in this environment?