  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 $x\in\{\infty, +,-,b\}$, and
$y\in\{\emptyset,b,+,-,\infty\}$ 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.
