Untangling trigonal diagrams

Let [Formula: see text] be a link of Conway’s normal form [Formula: see text], [Formula: see text], or [Formula: see text] with [Formula: see text], and let [Formula: see text] be a trigonal diagram of [Formula: see text] We show that it is possible to transform [Formula: see text] into an alternating trigonal diagram, so that all intermediate diagrams remain trigonal, and the number of crossings never increases.