Ok, now I understand what you are trying to do. I had no idea there was active research on that topic, I was lacking a piece of context to figure out why would

Ok, now I understand what you are trying to do. I had no idea there was active research on that topic, I was lacking a piece of context to figure out why would someone care. Your definition is equivalent to saying "TMs are not meaningfully different if their transition graphs are isomorphic", is that correct?