Non manifold boundary representations (b-reps) are increasingly used in Geosciences for a variety of applications (3D geographical information systems, basin modeling, geophysical processing, etc.). Meanwhile, the uncertainties associated with subsurface data make it desirable to modify such models efficiently. We present a method to deform locally a surface in a triangulated b-rep while maintaining a constant number of spatial regions in the model. This requires that the reshaped surface does not intersect the boundaries of its adjoining regions, which can be checked using existing collision detection algorithms. Besides, the non-manifold contacts must be updated after the modification, and the triangles must be altered, to maintain sealed regions. For this, we propose to parameterize locally the surfaces that the modified surface moves along. This parametric space is used to 1) constrain the displacement of the deformed surface border and, 2) re-triangulate in the plane the neighboring surfaces around the modified contacts. The method, tested in the context of an interactive graphical manipulator, is very efficient and independent from the deformation mechanism.