  Regarding three-dimensional (3D) topological insulators and semimetals as a
stack of constituent 2D topological (or sometimes non-topological) layers is a
useful viewpoint. Primarily, concrete theoretical models of the paradigmatic 3D
topological phases such as Weyl semimetal (WSM), strong and weak topological
insulators (STI/WTI), and Chern insulator (CI), are often constructed in that
way. Secondarily, fabrication of the corresponding 3D topological material is
also done in the same spirit; epitaxial growth technique is employed, making
the resulting sample in the form of a thin film. Here, in this paper we
calculate $\mathbb{Z}$- and $\mathbb{Z}_2$-indices and study evolution of the
topological properties of such thin films of 3D topological systems, making
also a comparative study of CI- vs. TI-type models belonging to different
symmetry classes in this respect. Through this comparative study we suggest
that WSM is to CI as STI is to WTI. Finally, to test the robustness of our
scenario against disorder and relevance to experiments we have also studied
numerically the two-terminal conductance of the system using transfer matrix
method.
