Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 4 / 21H / a / Solution

Let $i:L\hookrightarrow M$, $j:L\hookrightarrow N$, $r:M\hookrightarrow K$, and $s:N\hookrightarrow K$ be the inclusions. The Mayer–Vietoris sequence is the long exact sequence in homologyThe same sequence continues through degree zero, or uniformly in all degrees when written with reduced homology.