B\"{a}cklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property

New infinite number of one- and two-point B\"{a}cklund transformations (BTs) with explicit expressions are constructed for the high-order constrained flows of the AKNS hierarchy. It is shown that these BTs are canonical transformations including B\"{a}cklund parameter $\eta$ and a spectrality property holds with respect to $\eta$ and the 'conjugated' variable $\mu$ for which the point $(\eta, \mu)$ belongs to the spectral curve. Also the formulas of m-times repeated Darboux transformations for the high-order constrained flows of the AKNS hierarchy are presented.