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Summary To constrain seismic anisotropy under and around the Alps in Europe, we study SKS shear-wave splitting from the region densely covered by the AlpArray seismic network. We apply a technique based on measuring the splitting intensity, constraining well both the fast orientation and the splitting delay. 4 years of teleseismic earthquake data were processed, from 723 temporary and permanent broadband stations of the AlpArray deployment including ocean-bottom seismometers, providing a spatial coverage that is unprecedented. The technique is applied automatically (without human intervention), and it thus provides a reproducible image of anisotropic structure in and around the Alpine region. As in earlier studies, we observe a coherent rotation of fast axes in the western part of the Alpine chain, and a region of homogeneous fast orientation in the Central Alps. The spatial variation of splitting delay times is particularly interesting though. On one hand, there is a clear positive correlation with Alpine topography, suggesting that part of the seismic anisotropy (deformation) is caused by the Alpine orogeny. On the other hand, anisotropic strength around the mountain chain shows a distinct contrast between the Western and Eastern Alps. This difference is best explained by the more active mantle flow around the Western Alps. The new observational constraints, especially the splitting delay, provide new information on Alpine geodynamics.