The analogy between the evolution of a quasi-closed (decaying) two-level quantum system and the relativistic spin-¹/₂ motion in electric and magnetic fields is shown. The non-stationary equations for the 4-vector of a pseudo-spin describing the two-level system evolution are derived. In contrast with the well known three-dimensional model, the description is valid for arbitrary relaxation constant relations. In some limits the four-dimensional equations reduce to the optical Bloch ones. The 'energetic space' Lorentz invariance allows one to describe all possible solutions. Simple approximate quasi-stationary solutions are given for dephasing collisions and the region of their validity is determined. The Lorentz invariance of a Schrodinger equation with a non-Hermitian Hamiltonian is found and a set of four-component orthogonal eigenstates of the Dirac-type is constructed. Several examples of the utilisation of the four-dimensional formalism in laser-induced autoionisation, optics of anisotropic media, magnetic phenomena and K₀ meson, decay are present.