  With quark-antiquark annihilation and creation in the first Born
approximation, we study the reactions: $K \bar {K} \to K \bar {K}^\ast, ~K
\bar{K} \to K^* \bar{K}, ~\pi K \to \pi K^\ast, ~\pi K \to \rho K, ~\pi \pi \to
K \bar{K}^\ast, ~\pi \pi \to K^\ast \bar{K}, ~\pi \pi \to K^\ast \bar{K}^\ast,
~\pi \rho \to K \bar{K}, ~\pi \rho \to K^\ast \bar{K}^\ast, ~\rho \rho \to
K^\ast \bar{K}^\ast, ~K \bar{K}^\ast \to \rho \rho$, and $K^* \bar{K} \to \rho
\rho$. Unpolarized cross sections for the reactions are obtained from
transition amplitudes that are composed of mesonic quark-antiquark
relative-motion wave functions and the transition potential for quark-antiquark
annihilation and creation. From a quark-antiquark potential that is equivalent
to the transition potential, we prove that the total spin of the two final
mesons may not equal the total spin of the two initial mesons. Based on flavor
matrix elements, cross sections for some isospin channels of reactions can be
obtained from the other isospin channels of reactions. Remarkable temperature
dependence of the cross sections is found.
