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We re-examine possible dependencies on redshift of the spectral parameters ofblazars observed at very-high energies (VHEs) with Imaging AtmosphericCherenkov telescopes (IACTs). This is relevant to assess potential effects withthe source distance of the photon to axion-like particle (ALP) mixing, thatwould deeply affect the propagation of VHE photons across the Universe. Wefocus our spectral analysis on 38 BL Lac objects (32 high-peaked and 6intermediate-peaked) up to redshift $z\simeq 0.5$, and a small sample of 5 FlatSpectrum Radio Quasars up to $z=1$ treated independently to increase theredshift baseline. The 78 independent spectra of these sources are first of allcarefully corrected for the gamma-gamma interaction with photons of theExtragalactic Background Light, that are responsible for the majorredshift-dependent opacity effect. Then, the corrected spectra are fitted withsimple power-laws to infer the intrinsic spectral indices $\Gamma_{\rm em}$ atVHE, to test the assumption that such spectral properties are set by the localrather than the global cosmological environment. We find some systematicanti-correlations with redshift of $\Gamma_{\rm em}$ that might indicate,although with low-significance, a spectral anomaly potentially requiring arevision of the photon propagation process. More conclusive tests with higherstatistical significance will require the observational improvements offered bythe forthcoming new generation of Cherenkov arrays (CTA, ASTRI, LHAASO).

Revisiting the evidences for spectral anomalies in distant blazars: new data on the photon-ALP mixing