Here's some thoughts on common equipment for Axe:
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Vanguard: Everyone and their pet grandma likes to buy some of these. But are they worthwhile? The first sure can be when mixed in with your skills, there's great synergy there. But there's no reason to be a vanguard Axe. Laugh at everyone who buys three or four of these, there's much better items.
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Heart of Tarrasque: A fantastic choice in DOTA. Works well if you've gotten your vanguard, and possibly other tanking items. Experienced players won't go after Mogul first due to his being much harder to kill - but other people will. Making an unkillable tanker Axe works extremely well during pub stomps.
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Blink Dagger: Helps you aim your taunt much better. You can't go wrong buying this item unless your teammates are horrible.
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Shiva's Guard: An extra nuke and helps slow. It's an uncommon Axe item, but might be a better choice than an assault cuirass. It all depends on how the DOTA game is going for your allies.
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Lifesteal: It's nice, but you should save it for an afterthought. Try to grab items that have synergy with your skills first. Sure, you expect to get hit (& want to be for counter helix), but reduce the damage with blocking instead. You need to do serious damage DPS before life steal works well on him.
* Butterfly: Evasion is not good on this hero. Any Mogul Khan guide that might tell you otherwise without proof isn't one you should be listening to.
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Dagon: Very uncommon unless playing in pro DOTA games. Blink in, taunt, hit with a dagon energy burst, follow up with a Battle Hunger (if the enemy isn't running yet), then Culling Blade. Works extremely well.
Axe's core item is Phase Boot. (Vanguard, dagger, heart, all other are just optional)
Most enemies will stay constant distance between Axe.. or behind creeps to avoid his berserker call.. Phase Boot's activation ability is just simply perfect to solve this, no collision bypass creeps straight to the target and boom.
Just some random thought ~