This build is basically just so you can get the most damage out at all times. =) If i were you tho i'd be very careful because you tend to be relatively squishy. Your only health item is rod of ages and its not exactly a lot. That's why I have the runes for health and not just magic penetration and ability power. Yea, so this is my first build I would really appreciate any feedback :D

The Runes are set up so that you get a mix of magic penetration and health, so that when ur doing damage you're not too squishy and get killed by a Xin Zhao in 3 hits. The whole point is to give you enough survivability and penetration to get the maximum amount of damage possible without you dieing.

Yea, so the masteries are just set up in a basic fashion to give you what you need and improve your summoner spells a bit.

Now for the items, my favorite part :D. The reason that I build into cataclyst so early is for that sweet passive that lets you get some health and mana back when you level up. I did this so that you don't have to constantly go back and heal. The reason i get Abyssal Scepter instead of a percentage magic penetration is because at this point the enemy team won't have that much magic resist anyways, so at this point in the game a set amount is actually giving you a higher amount of magic penetration than a percentage magic penetration item would give you such as Void Staff, which you do get later in the game.
Now if you're doing good and getting a lot of kills, I'd say about 5 or 6 when your at this point, instead of the first rabadon, you can choose to get a mejai's if you want. This is a totally situational switch but if you're feeling pretty ballsy, then I say go for it.

Here are the reasons why I chose the summoner spells that I did:

Ghost: This spell allows you to escape if you really need to. It's also great for catching up to that low health champ you're chasing and getting that last shot in.

Flash: The way that I use this spells is so that after I use my flash frost and it lands, I flash in to ensure that I get my frostbite in for that double damage.

So farming. Big part of the game. What I like to do for farming is i just place down my ulti down on a wave of minions so that most of them are covered. Careful of your timing though because if you do it too late then the minions will move on and get out of your storm. (Note: I only farm this way after I get my Rod of Ages completed, before I just get last hits.)

BLUE GOLEM. I can't say it enough. It's so good on Anivia because if you have the blue golem buff, then your ulti basically takes no mana at all and you can just spam it if you would like. The way that I like to kill the blue golem is by putting down a wall right in front of it so that it gets pushed back and can't hit me and then I put my ulti down. Then I use the flash frost and frostbite combo and just auto attack. This should get you the golem in anywhere between 10 and 30 seconds, depending on your ap.