Human hemoglobin (HbA) is one of the prototypal systems used to investigate structure-function relationships in proteins. Indeed, HbA has been used to develop the basic concepts of protein allostery, although the atomic-level mechanism underlying the HbA functionality is still highly debated. This is due to the fact that most of the three-dimensional structural information collected over the decades refers to the endpoints of HbA functional transition with little data available for the intermediate states. Here, we report molecular dynamics (MD) simulations by focusing on the relevance of the intermediate states of the protein functional transition unraveled by the crystallographic studies carried out on vertebrate Hbs. Fully atomistic simulations of the HbA T-state indicate that the protein undergoes a spontaneous transition toward the R-state. The inspection of the trajectory structures indicates that the protein significantly populates the intermediate HL-(C) state previously unraveled by crystallography. In the structural transition, it also assumes the intermediate states crystallographically detected in Antarctic fish Hbs. This finding suggests that HbA and Antarctic fish Hbs, in addition to the endpoints of the transitions, also share a similar deoxygenation pathway despite a distace of hundreds of millions of years in the evolution scale. Finally, using the essential dynamic sampling methodology, we gained some insights into the reverse R to T transition that is not spontaneously observed in classic MD simulations.