  Based on our recent adaptation of the adiabatic limit construction to the
case of complex structures, we prove the fact, that we first dealt with in 2009
and 2010, that the deformation limiting manifold of any holomorphic family of
Moishezon manifolds is Moishezon. Two new ingredients, hopefully of independent
interest, are introduced. The first one canonically associates with every
compact complex manifold $X$, in every degree $k$, a holomorphic vector bundle
over $ \mathbb{C}$ of rank equal to the $k$-th Betti number of $X$. This vector
bundle shows that the degenerating page of the Fr\"olicher spectral sequence of
$X$ is the holomorphic limit, as $h\in\mathbb{C}^\star$ tends to $0$, of the
$d_h$-cohomology of $X$, where $d_h=h\partial + \bar\partial$. A relative
version of this vector bundle is canonically associated with every holomorphic
family of compact complex manifolds. The second new ingredient is a relaxation
of the notion of strongly Gauduchon (sG) metric that we introduced in 2009. For
a given positive integer $r$, a Gauduchon metric $\gamma$ on an $n$-dimensional
compact complex manifold $X$ is said to be $E_r$-sG if $\partial\gamma^{n-1}$
represents the zero cohomology class on the $r$-th page of the Fr\"olicher
spectral sequence of $X$. Strongly Gauduchon metrics coincide with $E_1$-sG
metrics.
