The nature of a substantial percentage (about one fifth) of hard X-ray sources discovered with the BAT instrument onboard the Neil Gehrels Swift Observatory (hereafter Swift) is unknown because of the lack of an identified longer-wavelength counterpart. Without such follow-up, an X-ray catalogue is of limited astrophysical value: we therefore embarked, since 2009, on a long-term project to uncover the optical properties of sources identified by Swift by using a large suite of ground-based telescopes and instruments. In this work, we continue our programme of characterization of unidentified or poorly studied hard X-ray sources by presenting the results of an optical spectroscopic campaign aimed at pinpointing and classifying the optical counterparts of 35 hard X-ray sources taken from the 70-month BAT catalogue. (...) With the use of optical spectra taken at six different telescopes we were able to identify the main spectral characteristics (continuum type, redshift, and emission or absorption lines) of the observed objects, and determined their nature. We identify and characterize a total of 41 optical candidate counterparts corresponding to 35 hard X-ray sources given that, because of positional uncertainties, multiple lower energy counterparts can sometimes be associated with higher energy detections. We discuss which ones are the actual (or at least most likely) counterparts based on our observational results. In particular, 31 sources in our sample are active galactic nuclei: 16 are classified as Type 1 (with broad and narrow emission lines) and 13 are classified as Type 2 (with narrow emission lines only); two more are BL Lac-type objects. We also identify one LINER, one starburst, and 3 elliptical galaxies. The remaining 5 objects are galactic sources: we identify 4 of them as cataclysmic variables, whereas one is a low mass X-ray binary.
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