Anivia Mid

I've been playing League since May. All of my friends that got me playing are Diamond and Gold, and I can now keep up with them. I started playing ranked a little earlier then I should have, and got demoted down to Bronze because of it. I've finally gotten good enough to start climbing a bit. I recently bought Anivia and am looking for any tips to help me carry harder with her, make plays, etc...
As of right now I'm building Tear, then RoA, finishing Archangels, then usually zhonyas and Liandry's. Abyssal sometimes. I've been thinking about maybe Lich Bane, but like... she doesn't really need it. Are there items I'm just not thinking of? (I build tankier if I'm behind.) Also, I tried Mejai's once. I got 25 stacks and did damage af, but like... early pre 4 game was like... so mana hungry I almost couldn't do it. I haven't tried it since.
I'm starting Q and maxing E. Running the Deathfire Touch keystone. Scaling AP blues, AP quints, Magic Pen red, and Armor/Health yellows depending on …
As of right now I'm building Tear, then RoA, finishing Archangels, then usually zhonyas and Liandry's. Abyssal sometimes. I've been thinking about maybe Lich Bane, but like... she doesn't really need it. Are there items I'm just not thinking of? (I build tankier if I'm behind.) Also, I tried Mejai's once. I got 25 stacks and did damage af, but like... early pre 4 game was like... so mana hungry I almost couldn't do it. I haven't tried it since.
I'm starting Q and maxing E. Running the Deathfire Touch keystone. Scaling AP blues, AP quints, Magic Pen red, and Armor/Health yellows depending on …