It is simultaneously the same axe and not the same axe. In a strict material sense, the final axe bears no relationship to the OG axe but in the figurative sense it is the same axe.

We must accept this paradox in the same way we must accept that our bodies are in a constant state of renewal and the person we were seven years ago has been completely renewed at a cellular level (maybe bones are exempt but brain cells don't last forever). We tend to think of ourselves as a continuous process and our identity persists and is stable. On the other hand, it's easy to argue that we are not the same person as we were seven years ago, we have grown and changed physically and spiritually. Only our identity documents contend that our identity is static. We seek stability and certainty everywhere and find it nowhere. If we can accept the ever changing nature of the universe at large we can find solace in constant change because that's how it will always be.