We analyzed the general form of all polarization effects in the H-3 + He-3 --> d(2)H + He-4 reaction. For this aim, we parametrized the spin structure of the full amplitude in terms of the transverse amplitudes which describe the different transitions between initial and final states, which in turn are differed by projections of nuclei spins along the normal to the reaction plane. The isospin invariance of the strong interaction generates definite symmetry properties of the transverse amplitudes relative to the change cos theta-->-cos theta, where theta is the deuteron production angle in the c.m.s. We found all symmetry relations for the polarization observables in the H-3 + He-3 --> d(2)H + He-4 reaction, which are the generalized form of the well-known Barshay-Temmer theorem. We consider the one-, two-, and triple-spin correlations in H-3 +He-3 --> d(2)H + He-4. For analysis of the triple-spin correlations, we focus on the structure functions formalism and show that a set of 41 structure functions describes all such correlations. Isospin invariance simplifies the spin structure of the full amplitude at theta=90 degrees; therefore, we calculated all polarization observables for this special kinematics.