  We study germs of analytic maps $f:(X,S)\rightarrow(\mathbb{C}^p,0)$, when
$X$ is an ICIS of dimension $n<p$. We define an image Milnor number,
generalizing Mond's definition, $\mu_I(X,f)$ and give results known for the
smooth case such as the conservation of this quantity by deformations. We also
use this to characterise the Whitney equisingularity of families of corank one
map germs $f_t\colon(\mathbb{C}^n,S)\to(\mathbb{C}^{n+1},0)$ with isolated
instabilities in terms of the constancy of the $\mu_I^*$-sequences of $f_t$ and
the projections $\pi\colon D^2(f_t)\to\mathbb{C}^n$, where $D^2(f_t)$ is the
ICIS given by double point space of $f_t$ in $\mathbb{C}^n\times\mathbb{C}^n$.
The $\mu_I^*$-sequence of a map germ consist of the image Milnor number of the
map germ and all its successive transverse slices.
