The Perseus OB1 association hosts one of the most populous groupings of blue and red supergiants (Sgs) in the Galaxy. We discuss whether the massive O-type and blue/red Sg stars located in the Per OB1 region are members of the same population and examine their binary and runaway status. We gathered a total of 405 high-resolution spectra for 88 suitable candidates around 4.5 deg from the center of the association, and compiled Gaia DR2 astrometry for all of them. This was used to investigate membership and identify runaway stars. By obtaining high-precision radial velocity (RV) estimates, we investigated the RV distributions of sample and identified spectroscopic binaries (SBs). Most of the investigated stars belong to a physically linked population located at d = 2.5$pm$0.4 kpc. We identify 79 confirmed or likely members, and 5 member candidates. No important differences are detected in the distribution of parallaxes for stars in h and X Persei or the full sample. On the contrary, most O-type stars seem to be part of a differentiated population in terms of kinematical properties. In particular, the percentage of runaways among them (45%) is considerable higher than for the more evolved targets (that is below 5% in all cases). A similar tendency is also found for the percentage of clearly detected SBs, which already decreases from 15% to 10% when comparing the O star and B Sg samples, respectively, and practically vanishes in the cooler Sgs. All but 4 stars in our working sample can be considered as part of the same (interrelated) population. However, any further attempt to describe the empirical properties of this sample of massive stars in an evolutionary context must take into account that an important fraction of the O stars is - or has likely been - part of a binary/multiple system. In addition, some of the other more evolved targets may have also been affected by binary evolution.
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