$\newcommand{\R}{\mathbf R}$ Let $x$ and $y$ be distinct points in $\R^n$ and $B$ be an open ball containing both $x$ and $y$. Let $i:(\R^n, \R^n-B)\to (\R^n, \R^n-x)$ and $j:(\R^n, \R^n- B)\to (\R^n, \R^n-y)$ be inclusions.
We know that $i_*:H_n(\R^n, \R^n-B)\to H_n(\R^n, \R^n-x)$ and $j_*:H_n(\R^n, \R^n-B)\to H_n(\R^n, \R^n-y)$ are isomorphisms.
Let $[B]$ denote a generator of $H_n(\R^n, \R^n-B)$ and $\tau:\R^n\to \R^n$ be the translation which takes $x$ to $y$.
Question. Does $\tau_*:H_n(\R^n, \R^n-x)\to H_n(\R^n, \R^n-y)$ satisfy $\tau_*(i_*[B])=j_*[B]$?
The motivation behind my question is that generators at $x$ and $y$ induced from the ball $B$ are declared as "consistent" when we attempt to define the notion of orientation using homology. I was wondering is the generator $\tau_*\mu_x$ at $y$ gotten by using a generator $\mu_x$ at $x$ is consistent with $\mu_x$.