Anivia is a mana hog. The mastries reflect this, as well as the early game items. The RoA needs time to stack up, so it is gotten before the Rabadons, however if you are having a hard time fighting, feel free to get the extra AP of the raba first. The AA gives you a boatload of mana AND Ap, but some people do not like the item. Feel free to substitute void staff or Abyssal instead.