  Any amicable pair \phi, \psi{} of Sturmian morphisms enables a construction
of a ternary morphism \eta{} which preserves the set of infinite words coding
3-interval exchange. We determine the number of amicable pairs with the same
incidence matrix in $SL^\pm(2,N)$ and we study incidence matrices associated
with the corresponding ternary morphisms \eta.
