Finite determinacy and stability of flatness of analytic mappings
  It is proved that flatness of an analytic mapping germ from a complete intersection is determined by its sufficiently high jet. As a consequence, one obtains finite determinacy of complete intersections. It is also shown that flatness and openness are stable under deformations. 
Janusz Adamus and Hadi Seyedinejad
math.CV math.AC