  We employ ab-initio electronic structure calculations to investigate the
charge-density waves and periodic lattice distortions in bilayer 2H-NbSe$_2$.
We demonstrate that the vertical stacking can give rise to a variety of
patterns that may lower the symmetry of the CDW exhibited separately by the two
composing 1H-NbSe$_2$ monolayers. The general tendency to a spontaneous
symmetry breaking observed in the ground state and the first excited states is
shown to originate from a non-negligible inter-layer coupling. Simulated images
for scanning tunnelling microscopy (STM) as well as diffraction/scattering
patterns show signatures of the different stacking orders. This may not only be
useful to reinterpret past experiments on surfaces and thin films, but may also
be exploited to devise ad-hoc experiments for the investigation of the stacking
order in 2H-NbSe$_2$. We anticipate that our analysis does not only apply to
the 2H-NbSe$_2$ bilayer, but is also relevant for thin films and bulk, whose
smallest centro-symmetric component is indeed the bilayer. Finally, our results
illustrate clearly that the vertical stacking is not only important for 1T
structures, as exemplified by the metal-to-insulator transition observed in
1T-TaS$_2$, but seems to be a general feature of metallic layered transition
metal dichalcogenides as well.
