For a given acyclic graph $G$, a topological sort is an ordering $v_1, \dots, v_n$ of the vertices such that the arrows in the graph are all directed forward under that ordering.
Question: can all topological orders of a graph $G$ be obtained from a single ordering by iteratively swapping two vertices that are not connected by an edge?
Motivation. In a certain context I am trying to prove that all topological sorts of an acyclic graph are in fact "equivalent". I want to do this by comparing $v_1, \dots, v, v', \dots v_n$ and $v_1, \dots, v', v, \dots v_n$ where there is no edge between $v,v'$.