Foliations which are limits of fibrations

On a closed oriented manifold M, a codimension one foliation F which is limit of a sequence of isotopic compact foliations (ξn)n∈N it is either a compact foliation isotopic to ξ0 or a non-compact foliation almost without holonomy. In the last case, the limit foliation F must have compact leaves and all leaves are proper. We describe a method to construct all these foliations when the manifold has dimension 3.