  Theoretically, bound binaries of massive black holes are expected as the
natural outcome of mergers of massive galaxies. From the observational side,
however, massive black hole binaries remain elusive. Velocity shifts between
narrow and broad emission lines in quasar spectra are considered a promising
observational tool to search for spatially unresolved, dynamically bound
binaries. In this series of papers we investigate the nature of such candidates
through analyses of their spectra, images and multi-wavelength spectral energy
distributions. Here we investigate the properties of the optical spectra,
including the evolution of the broad line profiles, of all the sources
identified in our previous study. We find a diverse phenomenology of broad and
narrow line luminosities, widths, shapes, ionization conditions and time
variability, which we can broadly ascribe to 4 classes based on the shape of
the broad line profiles: 1) Objects with bell-shaped broad lines with big
velocity shifts (>1000 km/s) compared to their narrow lines show a variety of
broad line widths and luminosities, modest flux variations over a few years,
and no significant change in the broad line peak wavelength. 2) Objects with
double-peaked broad emission lines tend to show very luminous and broadened
lines, and little time variability. 3) Objects with asymmetric broad emission
lines show a broad range of broad line luminosities and significant variability
of the line profiles. 4) The remaining sources tend to show moderate to low
broad line luminosities, and can be ascribed to diverse phenomena. We discuss
the implications of our findings in the context of massive black hole binary
searches.
