Verdier quotients of homotopy categories

We study Verdier quotients of diverse homotopy categories of a full additive subcategory $\mathcal{E}$ of an abelian category. In particular, we consider the categories $K^{x,y}(\mathcal{E})$ for $x\in \{\mathrm{\infty },+,-,b\}$, and $y\in \{\mathrm{\varnothing },b,+,-,\mathrm{\infty }\}$ the homotopy categories of left, right, unbounded complexes with homology being $0$, bounded, left or right bounded, or unbounded. Inclusion of these categories give a partially ordered set, and we study localisation sequences or recollement diagrams between the Verdier quotients, and prove that many quotients lead to equivalent categories.