# Extension of a null homotopic map to the mapping cone - unique up to homotopy equivalence?

Let $$\alpha : A \xrightarrow{} B$$ be a map of chain complexes. If $$\alpha$$ is chain homotopic to the zero map via a homotopy $$h$$, it is well known that the map $$h$$ extends to a chain map $$M(\alpha) \xrightarrow{} B$$.

My question is, for two different null homotopies , are the two resulting extensions $$M(\alpha) \xrightarrow{} B$$ chain homotopy equivalent?