What is equivalent capacitance of circuit between points A and B?  

Since a middle arm which connect the upper short the circuit. So, it will neglected.

The effective circuit is shown in figure. 
 The capacitance of upper series,
$$\begin{gathered} \frac{1}{C_{eq}}=\frac{1}{1}+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}\mathrm{......}\infty \\ \therefore C=\frac{2}{3}\mu C \\ {C}_{AB}=2C=2\times \frac{2}{3}\mu F \\ {C}_{AB}=\frac{4}{3}\mu F \end{gathered}$$