How do you know the fishless cycle in the first tank worked if you don't have a test kit? Did you take water to an LFS to be tested? Can't you go back to the same one? I don't know how sensitive axolotyls are but I certainly don't bother cycling betta tanks. In fact I don't for guppies, endlers, bristlenose, platys, or swordtails Some species are more sensitive than others I guess. If you want to be sure that your tank is in fact cycling and not simply sitting there getting older, then you really need to get your own test kits. You want to be able to see the ammonia rising, then falling away, then nitrite appearing then nitrate. And all this is so that you know that your filter will be able to cope with the bio load that you're going to put in there. If your filter is big enough and you're not overloading your tank, it shouldn't be necessary to cycle the filter before you add fish. The tank will go through a much more natural cycle using fish poop to feed the filter bacteria. As long as you're doing water changes everything should be fine.