  The two partition functions $p_\omega(n)$ and $p_\nu(n)$ were introduced by
Andrews, Dixit and Yee, which are related to the third order mock theta
functions $\omega(q)$ and $\nu(q)$, respectively. Recently, Andrews and Yee
analytically studied two identities that connect the refinements of
$p_\omega(n)$ and $p_\nu(n)$ with the generalized bivariate mock theta
functions $\omega(z;q)$ and $\nu(z;q)$, respectively. However, they stated
these identities cried out for bijective proofs. In this paper, we first define
the generalized trivariate mock theta functions $\omega(y,z;q)$ and
$\nu(y,z;q)$. Then by utilizing odd Ferrers graph, we obtain certain identities
concerning to $\omega(y,z;q)$ and $\nu(y,z;q)$, which extend some early results
of Andrews that are related to $\omega(z;q)$ and $\nu(z;q)$. In virtue of the
combinatorial interpretations that arise from the identities involving
$\omega(y,z;q)$ and $\nu(y,z;q)$, we finally present bijective proofs for the
two identities of Andrews-Yee.
