Topological String Partition Function on Generalised Conifolds

We show that the partition function on a generalised conifold $C_{m,n}$ with $\left(\genfrac{}{}{0px}{}{m+n}{m}\right)$ crepant resolutions can be equivalently computed on the compound du Val singularity $A_{m+n-1}\times \mathbb{C}$ with a unique crepant resolution.