  In the framework of axionically extended Einstein-Maxwell-aether theory we
study the structure of the electromagnetic field allowed by the anisotropic
cosmological spacetime platforms associated with the Bianchi models. These
models guarantee that the aether velocity possesses the shear, and we focus on
its role in the evolution of the axion-photon systems. In this short note we
discuss the extended master equations obtained under the assumption that the
square of the shear tensor is included in the potential of the axion field.
