  The aim of this book is to show that the use of f-analytic families of finite
type cycles (cycles having finitely many irreducible components, but not
compact in general) in a given complex space may be useful in complex geometry,
despite the fact that the corresponding functor is not, in general,
representable, in contrast to the compact case. This study leads to the notion
of strongly quasi-proper map which is characterized by the existence of a
geometric f-flattening which is a generalization of the Geometric Flattening
Theorem for proper holomorphic maps. As applications we prove an existence
theorem for meromorphic quotients of reduced complex spaces and a
generalization of the classic Stein factorization.
