We analyzed in a systematic way the public INTEGRAL observations spanning from December 2002 to September 2016, to investigate the hard X-ray properties of about 60 High Mass X-ray Binaries (HMXBs). We considered both persistent and transient sources, hosting either a Be star (Be/XRBs) or a blue supergiant companion (SgHMXBs, including Supergiant Fast X-ray Transients, SFXTs), a neutron star or a black hole. INTEGRAL X-ray light curves (18-50 keV), sampled at a bin time of about 2 ks, were extracted for all HMXBs to derive the cumulative distribution of their hard X-ray luminosity, their duty cycle, the range of variability of their hard X-ray luminosity. This allowed us to obtain an overall and quantitative characterization of the long-term hard X-ray activity of the HMXBs in our sample. Putting the phenomenology observed with INTEGRAL into context with other known source properties (e.g. orbital parameters, pulsar spin periods) together with observational constraints coming from softer X-rays (1-10 keV), enabled the investigation of the way the different HMXB sub-classes behave (and sometimes overlap). For given source properties, the different sub-classes of massive binaries seem to cluster in a suggestive way. However, for what concerns supergiant systems (SgHMXBs versus SFXTs), several sources with intermediate properties exist, suggesting a smooth transition between the two sub-classes.
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