  We use a Heegaard splitting of the topological 3-sphere as a guiding
principle to construct a family of its noncommutative deformations. The main
technical point is an identification of the universal C*-algebras defining our
quantum 3-spheres with an appropriate fiber product of crossed-product
C*-algebras. Then we employ this result to show that the K-groups of our family
of noncommutative 3-spheres coincide with their classical counterparts.
