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Anivia Build Guide by StrayKat
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-(9)Marks of Insight, is pretty much self explanatory, in the long runs, it will help you with your magic damage, as any good player would do when playing against spellcasters will build magic resistance.
-(9)Seals of Clarity, Anivia is a pretty mana starved beast if not you don't control your mana usage, I find myself at a loss of mana to help teamfights or finish of enemies due to lack of experience. To counteract this, I use mana regen/lvl coupled with mana regen items to ensure I always have something to throw when need be.
-(9)Glyphs of Force, This itself is to help Anivia do damage as she progresses in level. I find that if you build mana regen items, you often lack damage you need to remain as a threat to your enemies. What these glyphs here does is to allow you to do decent amount of damage while building mana regen items in the beginning.
Flash-This allows you to create a distance from ganks as well as focus fire if need be in team fights. This will also allow you to close gaps on enemies trying to escape from you.
Ghost-Allows you to reach teamfights much quicker as well as continue your combos of icy fury skills.
For Offensive Summoner skills, I would pick Ignite, good for finishing off healers/kills.
Exhaust is also a decent team fight as it allows your team to catch up if you are too far ahead as well as allow you to continue your combos on an enemy running away. It could also be used as a defensive skills as well when fighting against any hard core dps champions or for running away from them.
Utility, only two I can think of are heal and teleport. Like I said, Anvia is a champion deadliest when she is with her teammates. Being able to save a teammate or joining in a fight could ultimately change the flow of a game.