  A $K$-equivalent map between two smooth projective varieties is called simple
if the map is resolved in both sides by single smooth blow-ups. In this paper,
we will provide a structure theorem of simple $K$-equivalent maps, which
reduces the study of such maps to that of special Fano manifolds. As
applications of the structure theorem, we provide examples of simple
$K$-equivalent maps, and classify such maps in several cases, including the
case of dimension at most $8$.
