In conclusion, we have carried out a detailed study of the equation of state of a Fermi gas in the BEC-BCS crossover using FN-DMC techniques. In the BCS regime and in the unitary limit our results are in agreement with known perturbation expansions and with previous FN-GFMC calculations [CCPS03,CPCS04], respectively. In the BEC regime, we recover the equation of state of a gas of composite bosons with repulsive effective interactions which are well described by the molecule-molecule scattering length recently calculated in Ref. [PSS04].