  This paper studies complex cobordisms between compact, three dimensional,
strictly pseudoconvex Cauchy-Riemann manifolds. Suppose the complex cobordism
is given by a complex 2-manifold X with one pseudoconvex and one pseudoconcave
end. We answer the following questions. What is the relation between the
embeddability of the pseudoconvex end and the embeddability of the
pseudoconcave end of X? Do all CR-functions on the pseudoconvex end of X extend
to holomorphic functions on the interior of X?
  We prove that embeddability of a strictly pseudoconvex Cauchy-Riemann
3-manifold is not a complex-cobordism invariant. We show that a new phenomenon
occurs: there are CR-functions on the pseudoconvex end that do not extend to
holomorphic functions on X. We also show that the extendability of the
CR-functions from the pseudoconvex end is necessary but not sufficient for
embeddability to be preserved under complex cobordisms.
