Connected sum of a smooth manifold with itself is the boundary of another manifold

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.

The symbol $$\natural$$ denotes the boundary connected sum in this case. This is defined as follows.
Let $$M$$ and $$N$$ be $$d$$-manifolds with nonempty boundaries $$\partial M$$ and $$\partial N$$. Fix two $$(d-1)$$-disks embedded in the boundaries $$D^{d-1}\subset \partial M \subset M$$ and $$D^{d-1} \subset \partial N \subset N$$. Then $$M\natural N$$ is obtained by gluing the embedded disks of $$M$$ and $$N$$ together. In the oriented setting, this should be done such that they are glued together along an orientation-reversing homeomorphism.