Rigid isotopy of maximally writhed links

This is a sequel to the paper \cite{MO-mw} which identified maximally writhed algebraic links in $\rp^3$ and classified them topologically. In this paper we prove that all maximally writhed links of the same topological type are rigidly isotopic, i.e. one can be deformed into another with a family of smooth real algebraic links of the same degree.