  In this paper we consider the definition of " monodromy of an angle valued
map" based on linear relations as proposed in Burghelea-Haller (3). This
definition provides an alternative treatment of monodromy and computationally
an alternative calculation of the "Jordan cells", topological persistence
invariants of a circle valued maps introduced in Burghelea-Day (2).
  We give a new geometric proof that the monodromy is actually a homotopy
invariant of a pair consisting of a compact ANR and an integral degree one
cohomology class without any reference to the infinite cyclic cover associated
to cohomology class as in (3), or to the graph representation associated an
angle valued map defining the cohomology class as in (2).
  Most important, we describe an algorithm to calculate the monodromy for a
simplicial angle valued map defined on a finite simplicial complex, providing a
new algorithm for the calculation of the Jordan cells of the map, shorter than
the one proposed in (2).
  We indicate the computational usefulness of "Jordan cells", and in particular
of the proposed algorithm, for the calculation of other basic topological
invariants of the pair.
