I have found that frozen heart is a really great item for Anivia as its passive makes killing you in egg form harder, it also boosts the Archangel staff since it gives mana.
(random item recommendation)

Hey thanks for reply.

I edited it a bit. I am still a bit experementating with Anivia and I will update the build as often as possible to get it more detailed.

i've got to say, this build is undetailed and is a typical stack archangels staff's and hope for a good game and a noob enemy team,
i'd reccomend putting in a section about Anivias easter eggs, such as eggport and the timing on your Q to double hit them and stun.

at low levels the wall is useless considering your damage is nothing, specially with your mana useage (which brings up the mana crystal over meki pendant debate with meki pendant requiring patience but longer laning possibilites) i'd get it at lvl 12/11 so that you can pump your damage up as high as possible.
i'd also reccomend starting with boots first above all else since anivia is the squishiest character in the game and while having a egg, you cannot do anything while inside it, so boots would help you to escape skillshots (great help in mid)