We intend to study, for the first time, the role that neutron star (NS) interior physics and gravitational wave (GW) torques have in the spin evolution of accreting millisecond X-ray pulsars (AMXPs). Accreting NSs, and AMXPs in particular, are one of the most interesting laboratories to study the physics of compact objects and a potentially interesting source of GWs. There is, however, currently a ...