During the transport of oxygen Fe and Cu plays a vital role but why not other transition metals like Co, Mn, and others, what is the reason behind this?
The main reasons are the chemical properties and natural abundance. Co is also able to reversibly bind O2, but cobalt is not very abundant, about 2500 times less than iron. Copper is the 25th most abundant element in the earth's crust. Iron is the fourth most abundant element.