Does the transfer of matter occur during the propagation of a transverse wave?

To begin with, let us recall what transverse waves are, in them oscillations occur perpendicular to the direction of their propagation. in other words, the particles will move relative to each other, while they will oscillate in an upright position. We can confidently state that the shear wave is a shear wave. But one should not forget the fact that during the propagation of a transverse wave, the transfer of matter does not occur, but the transfer of energy takes place.