I don't know if you updated your guide yet, but chills from other characters don't affect Frost Bite.
And for Charm's post above me, I take it you don't realize that slows DON'T stack in LOL. What you'd end up getting is the 30% slow on Frostbite, and no returns on your other skills. (this is because your other skills slow for a higher % for longer. Therefore as slows do normally in this game, the highest % lasts its duration followed by any lesser slows that go beyond the first slow's duration.)
As for the guide itself, I don't know how anyone could justify wasting money on a Doran's item...they are just so bad and don't build into anything. I'd rather take my Saph --> Cata early. The reason why it's useless is, the hp is kinda silly, as you already have an EGG and shouldn't really be thinking about going offensive until you get your bread and butter initiator that is your ult. The mana regen is also not entirely the best because you won't really be using your mana much early on for it to matter and at level 6 you will already have other items to suppliment. The AP is nice, but as I have said before, you don't start being more active in getting kills until you have your full skillset of setups for Frostbite, which by then you'll have other items for AP.
*oh found something else*
You say you should be "harassing with Flash Frost" early, and never land the Frost bite until you can ensure heavy damage. My question is this. How exactly are you going to be harassing even semi-decent players with a very slow moving nuke that has a really long cooldown until later levels AND costs a ton of mana? Not taking my personal play into account, all the good Anivia's I've played with and against can all agree that you sit on your ass and farm early on and abuse your 600 range attack and wait for a quick FF--> FB setup. FF is useless without a follow-up FB. The mana --> damage is just terrible. Hero's with any regen will simply heal that amount by the time your cooldown for another FF is up. This guide would need some in-game footage as good support for your builds because right now it just seems like theory, that frankly would not work. You mention getting Revive as Anivia.....ORLY? And a guide like yours should probably include the Eggport strat, but I don't see it in here at all. It's definitely one of the best uses of a summoner skill possible, and it really only shines when used with Anivia.
*wow keep editing this with more stuff!*
Yeah, as the poster said two posts above me, you level flash frost first? I'm sorry but most players don't even get rank 2 until like level 8. Frostbite IS your damage. Flash Frost IS your setup. You need the chill effect. You have no ranks into Crystallize which is your best support ability. Getting it at level 4 is just critical to teamplay. I don't know how many games I've played where I got that extra level of FF at level 4 only to kick myself by botching a kill at level 6 because I couldn't wall them into my Glacial Storm. The ability to wall people in/split team fights/and snare people for 5 seconds (this assuming you have the Wall glitch down to a key, which might I had is quite hard) is way to valuable to wait until level 8.\
Anyway, I'm sorry for really railing into this and it prolly came off harsh, I tend to do that, but I'm glad to see more Anivia enthusiasts and I hope you don't take it too personally. GL in the future and I would be more than happy to hop on one day and play some matches with you to see your playstyle and may give any pointers I could give!
Second, yes I go Flash Frost early as possible due to FARMING purposes more than anything. It's allowed me on most occassions to have my Boots and Rod between 10-15 min in. I will however consider what you said about just dropping Doran's Ring, but the only reason I like the ring is the increased HP and the added AP. Also, by the time you get your Boots, now that they have Magic Pen instead, your Flash Frosts should be doing a good 25-40% of their HP with the trail+detonation at ranks 3-4. Depending on who you're laning against, of course.
For the mention on why no Wall early? Because in most games I tend to be the mid solo, so I will normally be in my lane until lvl 6-9, which happens very quickly on most occassions for me. I dont start ganking other lanes until I have my Rod of Ages, or I've pushed down the middle tower.
As for the Eggport strat? It's a bug, and I do not abuse bugs. It goes against my playstyle. The Rioters have even admitted it's a bug. As for the mention of Revive though? Well that needs updated. Lately I've found Clarity to probably be the best Summoner skill for her, supporting my early strategy of using high levels of Flash Frost. It's also great for her to have in team fights of course too. I did rank Revive up there strictly for the fact that on the rare occassion that you do die, you'll be able to jump right back in and defend what needs to be defended. It's helped many times when the enemy pushes and they've slaughtered your whole team, so you can quickly defend your turrets.
Anyways, I do thank you alot for the criticism. It's always accepted =P But I'm always ready to defend myself too. I will probably start buying the Ruby Crystal first before anything from now one however.