New relations between DIS sum rules

New relations between Bjorken polarized, Gross-Llewellyn Smith and Bjorken unpolarized sum rules are proposed. They are based on the ``universality'' of the perturbative and non-perturbative $\rm{1/Q^2}$ contributions to these sum rules. The letter facts can be deduced from the corresponding renormalon calculations. The similarity of $\rm{1/Q^2}$ corrections are checked by inspecting the numerical results obtained within several approaches.The discussed relations are in agreement with existing experimental data.Some possible new phenomenological applications are mentioned including estimates of not yet measured Bjorken unpolarized sum rule