  In [9], we observed Amalgamated R-transform Theory. Different from the
original definition of Voiculescu and Speicher, we define R-transforms of
operator-valued random variable(s) by operator-valued formal series. By doing
that we can establish Amalgamated R-transform calculus. In this paper, we will
concentrate on observing R-transforms on a tower of amalgamated noncommutative
probability spaces. We will consider the R-transform calculus and relation
between R-transforms on the tower and distributions with respect to the tower.
As application, we will observe the compatibility of the given tower and
commuting ladders of amalgamated noncommutative probability spaces
