Two links can be continuously deformed into each other iff any diagram of one can be transformed into a diagram of the other by a sequence of Reidemeister moves.
Reidemeister's Theorem
See also
Reidemeister MovesExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Reidemeister's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ReidemeistersTheorem.html