  The present material addresses several problems left open in the Trans. AMS
paper " Non-crossing cumulants of type B" of P. Biane, F. Goodman and A. Nica.
The main result is that a type B non-commutative probability space can be
studied in the framework of freeness with amalgamation. This view allows easy
ways of constructing a version of the S-transform as well as proving analogue
results to Central Limit Theorem and Poisson Limit Theorem.
