On his "Lectures on the h-cobordism theorem", Milnor characterizes the discs of dimention $n\ge 6$. The non trivial part is proving that if a simply connected manifold $W$ of dimentions $n\ge 6$ with $\partial W$ simply connected has the homology of a point, then it's diffeomorphic to a disc.
The proof is quite short: we remove a $n$-disc from $W$ and by excission $H_*(W\setminus \text{Int}(D_0),\partial D_0)\cong H_*(W,D_0)$, which is $0$ because $W$ has the homology of a point.
Then, by the h-cobordism theorem $(W,\partial W,\partial D_0)$ is a h-cobordism, so $W$ is diffeomorphic to $\partial D_0\times [0,1]$.
Now, this is the point that I don't fully understand: He says that $(W,\partial W,\emptyset)$ can be obtained from composing the cobordisms $(D_0,\partial D_0,\emptyset)$ and $(W\setminus \text{Int}(D_0),\partial W,\partial D_0)\cong \partial D_0\times [0,1]$. But the composition of these cobordisms depends on the isotopy class of the self diffeomorphism $\partial D_0\to \partial D_0$ we're using to paste the two collars, right? Are we using the fact that the diffeomorphism $\phi:(W,\partial W,\partial D_0)\to \partial D_0\times [0,1]$ can be chosen so that $\phi|_{\partial D_0}:\partial D_0\to \partial D_0\times \{0\}$ is the identity?