The documentation states “The image used when rendering the sprite.”. It’s not the best of description since what you get is the “atlas”/“tilesource”.
And even if the property referred to an individual image in the atlas there’s a problem with your conditional check:
if sprite.image == hash("axe-13") or hash("axe-14") or hash("axe-15") then
I’m guessing that you want to check is if sprite.image is one of “axe-13”, “axe-14” or “axe-15”? If that is indeed true then you need to write your check like this:
if sprite.image == hash("axe-13") or sprite.image == hash("axe-14") or sprite.image == hash("axe-15") then
What you could do is to use the normalised flipbook cursor: API reference (sprite)