Peskin & Schroeder, An Introduction to Quantum Field Theory, write at page 224
$$\int d^{4} x e^{i p \cdot x}\left\langle\Omega\left|T\left\{\phi(x) \phi\left(z_{1}\right) \cdots\right\}\right| \Omega\right\rangle $$ $$\underset{p^0\to+E_{\mathbf{p}}}{\sim}\frac{i}{p^{2}-m^{2}+i \epsilon} \sqrt{Z}\left\langle\mathbf{p}\left|T\left\{\phi\left(z_{1}\right) \cdots\right\}\right| \Omega\right\rangle\tag{7.37},$$
but I don't understand the meaning of this notation ($\sim$). At the beginning of section 7.2. Peskin & Schroeder also write
Here and throughout this section we use the symbol $\sim$ to mean that the poles of both sides are identical [...],
but I don't understand the meaning of this sentence.