Marar–Mond conjecture on good real perturbations

Let $f:(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$ admit a good real perturbation $f_s^{\mathbb{R}}$, meaning that the changes in homology caused by the perturbation can be observed in its real image. Let $f_s$ be the complexification of $f_s^{\mathbb{R}}$. Marar–Mond conjecture. The image of $f_s^{\mathbb{R}}$ and the image of $f_s$ are homotopy equivalent. The conjecture concerns the relationship between the topology of real perturbation images and their complexifications; the source abstract states that it is proved for singularities from $\mathbb{C}^n$ to $\mathbb{C}^{n+1}$, so it is solved in the setting asserted here.