Top: Unfolded average spectrum of the persistent emission from MAXI J1957+032. The blue curves represent Swift/XRT spectra, from the earliest observation (darkest blue) to the latest (lightest blue), fitted with the TBabs*powerlaw model (see Sect. 3.2.2). In the legend, Swift/XRT observations are labelled ‘SW’ followed by their Obs. ID (see Table A.1). The red curve shows the XMM-Newton/PN spectrum, fitted with TBabs*(thComp*bbodyrad) (see Sect. 3.2.1). Bottom: Residuals with respect to the adopted models.