  Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled
by an angle $\theta$ are constructed and then reduced to the two-component
Camassa--Holm model. Only three different independent classes of reductions are
encountered corresponding to the angle $\theta$ being 0, $\pi/2$ or taking any
value in the interval $0<\theta<\pi/2$. This construction induces B\"{a}cklund
transformations between solutions of the two-component Camassa--Holm model
associated with different classes of reduction.
