Fig. 2

Reidemeister moves of types 0, 1, 2, and 3, denoted \(\Omega _i,\, i=0,\dots ,3\). \(\Omega _0\) deforms one arc without changing crossings (not shown). Left, \(\Omega _1\) either adds one crossing to an isolated segment or deletes an isolated loop. In the middle, one of two parallel strands is slid either above or below the other by \(\Omega _2\). To the right: \(\Omega _3\) moves an arc across a crossing between two other arcs. By the usual right hand rule, the left most crossing in the picture of \(\Omega _1\) is negative and the other crossing in this picture is positive meaning that if you choose a direction of traversing of the curve the streamlines fulfill the right hand rule