  In this paper, based upon the basic theory for glued manifolds in M.W. Hirsch
(1976) \cite[Chapter 8, \S 2 Gluing Manifolds Together]{h}, we give a method of
constructing homeomorphisms between two small covers over simple convex
polytopes. As a result we classify, up to homeomorphism, all small covers over
a 3-dimensional prism $P^3(m)$ with $m\geq 3$. We introduce two invariants from
colored prisms and other two invariants from ordinary cohomology rings with
${\Bbb Z}_2$-coefficients of small covers. These invariants can form a complete
invariant system of homeomorphism types of all small covers over a prism in
most cases. Then we show that the cohomological rigidity holds for all small
covers over a prism $P^3(m)$ (i.e., cohomology rings with ${\Bbb
Z}_2$-coefficients of all small covers over a $P^3(m)$ determine their
homeomorphism types). In addition, we also calculate the number of
homeomorphism types of all small covers over $P^3(m)$.
