Suppose $M$ is a topological manifold without boundary. If $B$ and $B'$ are nicely embedded balls in $M$. Then, i've read somewhere that under certain conditions on the embedding using a bicollaring, we can always find homeomorphism $h:M\rightarrow M$ with $h(B)=B'$
What does nicely embedded balls mean? and how does one explisitly construct the homeomorphism? Is there a complete proof of this?
I guess if $M$ connected, pick points $p\in B$, $p'\in B'$. Sinse $M$ homogeneous, there exists a homeomorphism $f:M\rightarrow M'$ such that $f(p)=p'$. But I don't know how to extend to all of $B$ and $B'$.
By above I think we need to assume $M$ is connected too