Let $X\subset \mathbb{A}^4_\mathbb{C}$ be a three fold defined by the equation $xy-zw=0$
This variety has a singularity at origin of $\mathbb{A}^4_\mathbb{C}$
If we blow up this three fold in two ways i.e by the ideals $(x,z)$ and $(y,z)$, we can get two resolutions $Y_0\rightarrow X,Y_1\rightarrow X$ with exceptional curves $\mathbb{P}^1_\mathbb{C}$

How can I prove $Y_0$ and $Y_1$ are not isomorphic over $X$.

I would like to prove this claim in order to prove $X$ has no minimal resolution.