(a) Comparison of the transverse momentum spectrum d$^{2}N$/(d$p_{\rm T}$d$y$) of $\phi$-meson in non-single diffractive (NSD) p-Pb events, reconstructed via the decay channel into K$^+$K$^-$ by exploiting three different strategies for K identification: TPC only, TPC-TOF and no-PID. The reader can refer to Sec.3.1 for details on the PID selection and to Sec.3.2 for a description of the signal extraction procedure. The uncertainties are the sum in quadrature of statistical and systematic. A Levy-Tsallis function (see Eq.4.1) is used to fit the TPC-TOF spectrum in 0.3 < $p_{\rm T}$ < 10 GeV/$c$. (b) Ratio of each spectrum to the fit function, showing good agreement of the three PID strategies within uncertainties.