Circuit analysis of graphic equalizer
C2,C4,etc caps invert the voltage and thus impedance of these caps   in the -ve feedback loop of the filter and thus call Negative impedance converter (NIC) filters or Gyrators.

NIC: This reverses the voltage polarity or the current direction of the port and introduces a phase shift of 180° (inversion) between the voltage and the current for any signal generator. The two versions obtained are accordingly a negative impedance converter with voltage inversion (VNIC) and a negative impedance converter with current inversion (INIC)
GYRATOR:  An important property of a gyrator is that it inverts the current-voltage characteristic of an electrical component or network. In the case of linear elements, the impedance is also inverted. In other words, a gyrator can make a capacitive circuit behave inductively, a series LC circuit behave like a parallel LC circuit, and so on. It is primarily used in active filter design and miniaturization


if R1 = R2
\$V_{in+}/I_{R_1} = - R_{3}\$
Note in this EQ a -ve cap is used for an inductor.
\$ V_{in+}-V_{in-}=0\$ as always, when linear.
Note your schematic that you show,  has an (obvious) error, with the common line at bottom not grounded, as it should be...corrected below.

This equivalent circuit is shown above, except for values.