The crystallization mechanisms of sputtered Fe1-xCx amorphous thin films for three values of atomic carbon content x = 0.28, 0.30 and 0.32 are directly observed using hot stage transmission electron microscopy. Images recorded sequentially are used to track the change caused by heating. Observations concern the nucleation and the growth of iron carbides and their structural identification. Information is also given about their crystallochemistry. They belong to the family of interstitial carbides with carbon atoms located inside iron Triangular Prisms (TP). They are built either from TP Sheets (TPS) stacks deriving from the cementite θ-Fe3C or from TP Chains (TPC) arrangements deriving from the Eckström-Adcock Fe7C3 carbide. The sharp transition between dominant TPS and dominant TPC carbides formations is illustrated. Nucleation and growth processes of both types of carbides are discussed and focus is put on the TPC crystals. They are the first to be formed whatever carbon content of the specimen and really correspond to the dominant phase for the richest-carbon film. When they are less numerous, they can act as nucleation sites for TPS carbides and it is in situ illustrated during the crystallization of the poorest-carbon film where orientation relationships can be found between the TPC-Fe7C3 carbide and a TPS carbide close to the Hägg carbide χ-Fe5C2 The crystallization of Fe0.70C0.30 film corresponds to a particular case where TPC carbides and TPS carbides can coexist with the same composition.