  The propagation length of high-energy photons through the Universe is limited
by $e^+e^-$ pair production on the extragalactic background radiation. Previous
studies reported discrepancies between predicted and observed attenuation,
suggesting explanations in terms of new physics. However, these effects are
dominated by a limited number of observed sources, while many do not show any
discrepancy. Here, we consider the distribution in the sky of these apparently
anomalous objects, selected in two very different approaches: the study of
unphysical hardenings at distance-dependent energies in deabsorbed spectra of
TeV blazars, and the observation of ultra-high-energy air showers from the
directions of BL Lac type objects. In both cases, directions to the anomalous
sources follow the projected local distribution of galaxies: all the distant
sources, contributing to the anomalies, are seen through the local filament.
This matches the prediction of the proposed earlier explanation of the
anomalies based on mixing of photons with axion-like particles in the
filament's magnetic field. For ultra-high energies, this axion interpretation
may be tested by the search of primary gamma rays.
