2005 Mazda 3 SP2.3

I can not figure out what this hose is called. It has coolant running through it. Or at lease it did until the hose busted and emptied my radiator fluid all over my garage. I REALLY don't want to take it to a shop just to have a hose replaced but I can't figure out what I need to order.

Can someone help me out? A link to somewhere I can order a new one would be great.

 

Take the photo into the parts department of your local Mazda dealer.

 

^ this

 

That is a water pump by pass hose.