It is known that given a knot diagram we can transform it into a trivial unknot diagram by a series of Reidemeister moves. The key word is "series".

**Can we transform any knot diagram using a finite number of exclusively one of Reidemeister moves into a trivial unknot?** (given that we can deform its links in any way)

The immediate answer that comes up in my mind is "no", but I have no idea how to correctly prove it. Twist (type 1 Reidemeister move) and poke (type 2 Reidemeister move) moves, for example, decrease the number of crossings in a knot diagram, so a "greedy" way of thinking about this problem is that only first two Reidemeister moves can actually achieve it in a finite number of moves (guaranteed we can use unknot operations), and the third one can't.

It would be great if someone could provide some resources on further reading or point me into the right direction.