REPRESENTING 3-VARIEDADES AREA OF DEHN RELLENANTESSummary: It is a study of the representation of 3-variedades area of dehn rellenantes and diagrams johansson partners. This way of representing 3-variedades has its origins in work W. Haken and JM Montesinos. It examines in depth the problem of how to relate to one another the different representations of the same 3-variedad. In the main outcome of the work provides a complete system of hands that relate representations of the same 3-variedad. In addition, we study in detail other results already known and provided several examples and problems open.