In I2C communication, the Master sends data to the Slave and receives data from it. This communication occurs over clock edges, specifically the rising and falling edges. In the setup with pull-up resistors, it appears that the Master transfers data to the Slave at the falling dge and receives data from it at the rising edge

I want to clarify: during which clock edge does the Master transfer data to the Slave and receive data from it?"

 

It is level driven, not edge driven. Data is only allowed to change when the clock is low. Data, therefore, must be stable all the time the clock is high.