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When voltage is first applied to the circuit the first capacitor starts to charge and its voltage increases. When the voltage reaches the amount needed to cause the transistor to conduct it's like toggling a switch to short the other capacitor to ground. Then the other capacitor starts to charge until its voltage is high enough to switch its transistor and it shorts the other capacitor, which drops the voltage low enough to shut off the other transistor. Back and forth the capacitors short each other out by flipping the others switch.
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