there is a closed immersion $\mathbf{P}^1_ Z \to W$ whose composition with $b$ is the inclusion morphism $\mathbf{P}^1_ Z \to \mathbf{P}^1_ X$ and whose base change by $\infty $ is the composition $Z \to C_ ZX \to E \to W_\infty $ where the first arrow is the vertex of the cone.
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