  For a Koszul operad $\mathcal{P}$, there are several existing approaches to
the notion of a homotopy between homotopy morphisms of homotopy
$\mathcal{P}$-algebras. Some of those approaches are known to give rise to the
same notions. We exhibit the missing links between those notions, thus putting
them all into the same framework. The main nontrivial ingredient in
establishing this relationship is the homotopy transfer theorem for homotopy
cooperads due to Drummond-Cole and Vallette.
