Dear Allan,

This is the first draft of my part for the NY conference. 
I didn't put many examples as I should, this is due to the fact that I prefer to concentrate on the soundness of the three parameters deformation.
1) Fig 2 will be "delabelled" 
2) Theorem 4.1 and proposition 5.1 are general and new (up to my knowledge) I tailored them for the purpose, the proofs will be put in an annex.

Do not hesitate to make remarks (for the meanwhile I finish this paper).

Best regards
Gerard