For the first pair take $0 \longrightarrow \mathbb{Z} \stackrel{2}{\longrightarrow} \mathbb{Z} \longrightarrow \mathbb{Z} / 2\mathbb{Z} \longrightarrow 0$ and $0 \longrightarrow \mathbb{Z} \stackrel{3}{\longrightarrow} \mathbb{Z} \longrightarrow \mathbb{Z} / 3\mathbb{Z} \longrightarrow 0.$
For sequences with non-isomorphic first pairs you can use an infinite direct sum of $\mathbb{Z}$'s and include one or two copies of $\mathbb{Z}$. The quotient will be the infinite direct sum again so the second and third pairs are isomorphic but the first pair will be non-isomorphic.
Finally for non isomorphic central pairs take $0 \longrightarrow \mathbb{Z} / 2\mathbb{Z} \longrightarrow \mathbb{Z} / 2\mathbb{Z} \times \mathbb{Z} / 2\mathbb{Z} \longrightarrow \mathbb{Z} / 2\mathbb{Z} \longrightarrow 0$ and $0 \longrightarrow \mathbb{Z} / 2\mathbb{Z} \stackrel{2}{\longrightarrow} \mathbb{Z} / 4\mathbb{Z} \longrightarrow \mathbb{Z} / 2\mathbb{Z} \longrightarrow 0.$