ScalingStacks

Given a link $L$ in $\mathbb{R}^{3}$ we can take its generic projection on the plane. A generic projection is the one without triple points and double tangencies. An isotopy class of such projections is called a plane diagram of $L,$ or, simply, a diagram. The following four types of transformations of plane diagrams preserve the isotopy type of the associated link.

I. Addition/removal of a left-twisted curl:

II. Addition/removal of a right-twisted curl:

III. Tangency move:

IV. Triple point move:

$\square$