  We consider analytically and numerically an anisotropic spin-$\frac{1}{2}$
delta-chain (sawtooth chain) in which exchange interactions between apical and
basal spins are ferromagnetic and those between basal spins are
antiferromagnetic. In the limit of strong anisotropy of exchange interactions
this model can be considered as the Ising delta chain with macroscopic
degenerate ground state perturbed by transverse quantum fluctuations. These
perturbations lift the ground state degeneracy and the model reduces to the
basal XXZ spin chain in the magnetic field induced by static apical spins. We
show that the ground state of such model is ferrimagnetic. The excitations of
the model are formed by ferrimagnetic domains separated by domain walls with a
finite energy. At low temperatures the system is effectively divided into two
independent subsystems, the apical subsystem described by the Ising
spin-$\frac{1}{2}$ chain and the basal subsystem described by the XXZ chain
with infinite $zz$ interactions.
