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A lengthy explanation would be necessary. It will be difficult to follow.
When one transistor turns on, it shuts off the other.
The capacitors charge and discharge in a manner which alternately raises and lowers voltage at the bias terminals.
It will be easier to understand by watching a video.
I have a Youtube video which is an animated simulation of the astable multivibrator. It portrays the capacitors charging and discharging. It depicts current bundles moving through wires.
I believe it will aid in conceptualizing the principles of operation in this circuit.
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