I'd say this is a good start to a solid Anivia guide.

The items are not thoroughly explained - I would either provide explanations of why you selected each item and in the order you did, or reconsider your build choices. For example: why Rylai's when 2/3 of your damage spells slow, and is Maeja's really a good idea when you aren't doing well?

Beyond this I agree with many of your points, though I do not think you conserve your mana properly, as you neglect to mention Anivia's fantastic E + R combo. Q + E is nice damage, but considering how hard Q is use in most situations as well as its insane mana cost, its just not a viable harass. I think you will find you do better if you prioritize your W ahead of your Q and get really good at E + R harassing, as it uses much less mana and allows you to build more heavily into AP.

Also, this is just a matter of opinion, but Ignite as a necessity? While ignite will assist you with unexpected kills, I don't really think it is viable on Anivia, unless you are using it as a skill-crutch. Between your AoE slow, stun, and wall, you should really be in full control of your opponent when playing properly. I agree Flash is essential, but I personally think Anivia benefits from Teleport more than Ignite.

Nice start though, you'll have my +1 when you're finished!

Edit: The runes, err, yeah. Even if this is what you use, you shouldn't make the mistake of recommending it to other players! Magic penetration reds are a MUST, and health yellows of some sort are very much recommended over secondary AP.