The quantum dynamics of a system of three interacting identical spin-qubits with the XY Heisenberg exchange interaction between two nearest-neighbour spin-qubits is studied in the Markovian approximation with respect to the interaction between this system and the environment. A Lindblad formula with two physical mechanisms of the decoherence is used. Two different cases are considered simultaneously: three spin-qubits interact with three district baths of excitations or with one and the same common bath of excitations. The systems of rate equations are solved in the first-order approximation with respect to the small constants of decoherence.