  We consider the $M$-neighbor approximation in the problem of one-qubit pure
state transfer along the $N$-node zigzag and alternating spin chains governed
by the $XXZ$-Hamiltonian with the dipole-dipole interaction. We show that
always $M>1$, i.e., the nearest neighbor approximation is not applicable to
such interaction. Moreover, only all-node interaction ($M=N-1$) properly
describes the dynamics in the alternating chain. We reveal the region in the
parameter space characterizing the chain geometry and orientation which provide
the high-probability state-transfer. The optimal state-transfer probability and
appropriate time instant for the zigzag and alternating chains are compared.
