A density counterpart of the Scheepers covering property

We introduce a density counterpart of the Scheepers covering property ${\bigcup }_{\mathrm{f}\mathrm{i}\mathrm{n}}(\mathcal{O},\mathrm{\Omega })$ and study its relations to known combinatorial density property. In particular, we show that it is equivalent to the $M$-separability under the Near Coherence of Filters principle of Blass and Weiss.