Intuitive way to see pole/zero directly from schematic
First get an RLC nomograph and transparent or translucent paper.
Since adding log graphs of Z(f) becomes like linear superposition, you can then add up each node remembering that Av is impedance ratio on inverting side and 1+Av for non-Inverting side.   Pole zeros that combine multiple resistors and capacitors can be intuitively ignored at f near 0 and ∞ as open and short. 

(R1/(R2+C1))//C2 is can be a lead/lag circuit.  These are used in PLL filters and SMPS filters to have two ranges where the R ratios dominate the band no phase shift) This occurs when Zc is too low or too high compared to R to affect a change, which you can see on the nomograph.

Just identify which ratios you are using change colors for negative feedback where the slope inverts ( negative impedance conversion).
With practise you ad more parts and find the resonant frequency of RC circuits from phase cancellation where the -Zc = +Zc making band reject or band pass filters.

Q or -3dB BW is then the reactive/real impedance change or visa versa depending if series or shunt using negative impedance Caps ( -ve feedback) or inductors.