Did he upgrade the head and handle? If so, it’s still your grandpa’s axe. Did you upgrade the axe? It might now be an axe of your own making. If “same” is extended not just to refer to the materials, but refers to fourth-dimensional quantum axe states, the axe stops being your grandpas axe the moment your grandpa isn’t chopping with it, but becomes his axe any time he returns to use it.