  We consider the bulk algebra and topological D-brane category arising from
the differential model of the open-closed B-type topological Landau-Ginzburg
theory defined by a pair $(X,W)$, where $X$ is a non-compact Calabi-Yau
manifold and $W$ has compact critical set. When $X$ is a Stein manifold (but
not restricted to be a domain of holomorphy), we extract equivalent
descriptions of the bulk algebra and of the category of topological D-branes
which are constructed using only the analytic space associated to $X$. In
particular, we show that the D-brane category is described by projective matrix
factorizations defined over the ring of holomorphic functions of $X$. We also
discuss simplifications of the analytic models which arise when $X$ is
holomorphically parallelizable and illustrate these analytic models in a few
classes of examples.
