While searching connected sum, I got this page. I have a doubt with the notation $\natural$ that I don't know how to define formally. It says, given a smooth manifold $M$ one has $\partial(W\natural W)=M\sharp M$, here $W$ is the total space of the disk bundle of $M$. Also, if $\bullet$ denotes deleting a small embedded disk from the manifold then $(M_0 \sharp M_1)^\bullet = (M_0^\bullet) \natural (M_1^\bullet) \simeq M_0^\bullet \vee M_1^\bullet. $
Any reference for the notation $\natural$ will be helpful.