What do you build on Azir?
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rod of ages is great as a first item on him, after that I just build a mix os AP and defense. nashors tooth is best saved for a 3rd or 4th item for when you get more AP to back up the attack speed it gives your soldiers.
ROA should be your first item. I usualy build like this:
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Thoses are also good:
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I generally use Expession's build if I'm playing APC Azir -

Also a big fan of Tank Azir, tho -

Rod of Ages is definitely good, but so is Mana Regen. The thing about Azir is that there is multiple build paths and you can adapt to many scenarios.
Mana Regen or not? If you can depend on your Jungler giving you blue I'd go straight for Rod of Ages. If you can't, then early mana regen through either Athenes or Morellos is recommended.
Athenes or Morellos? Morellos gives you an earlier power spike because of the 20% cdr on its base components, but Athenes scales more into late game. Both are great picks. I usually Morellos because I want the early power spike.
What about Nashor's Tooth?
Azir community seems split on Nashor's Tooth. While you can't proc the passive the base stats are still good. Personally I prefer to not build Nashor's tooth as I feel like standard Mage AP items give me more damage. the AS you get from your passive is already plenty.
As a general rule of thumb ensure your soldiers pack a punch before building up your attack speed.
I pick up an early Nashor's tooth if I'm doing very well in lane, as the AS increase is insane if you've already got plenty of AP built up. However, if you're behind, make sure your soldiers pack a punch first.
When to buy CDR?
CDR is really good on Azir. Get it almost immediately. You power spike with CDR more than any other champ does with the same stat because of your passive. It also allows you to bully in lane far more effectively, gives you more security as your E will be up more often, and is just overall made of win.
My Typical Build Path
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(if mr) ->
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