  In recent joint works of the present author with M.Prasolov and V.Shastin a
new technique for distinguishing Legendrian knots has been developed. In this
paper the technique is extended further to provide a tool for distinguishing
transverse knots. It is shown that the equivalence problem for transverse knots
with trivial orientation-preserving symmetry group is algorithmically solvable.
In a future paper the triviality condition for the orientation-preserving
symmetry group will be dropped.
