  By using the density matrix renormalization group, we study the spin-liquid
phases of spin-$1/2$ XXZ kagome antiferromagnets. We find that the emergence of
spin liquid phase does not depend on the anisotropy of the XXZ interaction. In
particular, the two extreme limits---Ising (strong $S^z$ interaction) and XY
(zero $S^z$ interaction)---host the same spin-liquid phases as the isotropic
Heisenberg model. Both the time-reversal-invariant spin liquid and the chiral
spin liquid with spontaneous time-reversal symmetry breaking are obtained. We
show they evolve continuously into each other by tuning the second- and
third-neighbor interactions. At last, we discuss the possible implication of
our results on the nature of spin liquid in nearest neighbor XXZ kagome
antiferromagnets, including the most studied nearest neighbor spin-$1/2$ kagome
anti-ferromagnetic Heisenberg model.
