Time evolution of the flux and spectral parameters of V404 Cyg during the June 2015 flaring episodes. Green and blue symbols are unchanged with respect to Fig. 2. Red symbols highlight the parameters obtained fitting the data with a Comptonized model (compps) modified by variable absorption. The BIC model selection (see text) favours this model only for the spectra detected during the X-ray plateaus. For comparison, we also show the parameters obtained in the fits to these spectra fixing the absorption to interstellar values (grey symbols in panels b), c) and e). Panel a) source flux (20–200 keV) in units of 10^-8 erg cm^-2 s^-1. Panel b) optical depth, τ, Panel c) electron temperature, T_e. Panel d) N_H values obtained for the whole data set when leaving N_H as a free parameter; only when N_H ≳ 10²⁴ cm^-2 modifies substantially the spectral shape in the IBIS/ISGRI energy range, can this value be properly constrained in our spectral fits. This happens during the X-ray plateaus. Panel e) value for every fit.