a space isomorphic to $S^{p+q}$

Question

In one of the paper I have met that $$\mathbb{S}^{p+q} \cong \mathbb{S}^p \times \mathbb{R}^q \cup \mathbb{S}^{p-1}$$

I don't know how to deal with $\mathbb{S}^{p-1}$ sphere.

Are there any reference to this isomorphism?

Thanks in advance!