Two knot diagrams \(K\) and \(K'\) are called equivalent and denoted by \(K\sim K'\), if there is a finite sequence of diagrammatic moves (i.e. either Reidemeister moves or planar isotopy moves) \((K_n)_{n\in\mathbb N}\), such that
\[K=K_0\sim K_1\sim K_2\sim\ldots\sim K_n=K'.\]
In particular, the diagrammatic moves define an equivalence relation on knot diagrams.
Proofs: 1
Definitions: 1