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Fusion reactions in the deuterium cycle (D+D, D+T and D+3He) are the main nucleus-nucleus interactions which occur in tokamaks and stellerators. Fusion cross-sections and fusion reactivities have been reviewed and compared with experimental data from the last ENDF/B-VIII.0 cross-section library. Fusion reactivities have been estimated through a numerical integration of ENDF fusion cross-sections and compared with several formulations. Lawson criterion has been appplied to D+T fuel plasma and compared with several fusion reactors. As a conclusion, this shows that physical models for the astrophysical factor S(E) and bremstrahlung losses should be reviewed, in order to apply fusion to energy production in safety conditions.