  In a recent paper the quantum 2-sphere $S^2_q$ was described as a quantum
complex manifold. Here we consider several copies of $S^2_q$ and derive their
braiding commutation relations. The braiding is extended to the differential
and to the integral calculus on the spheres. A quantum analogue of the
classical anharmonic ratio of four points on the sphere is given, which is
invariant under the coaction of $SU_q(2)$.
