Modem 56k to Arduino R3, serial data

micnossub:
do the output signal on the second modem is the same as the input of the modem who transmit the data?

Not exactly the same. If there is no error then the characters sent to the transmitting modem will come out the other side. Errors can cause characters to get lost. Character timing may be changed because of buffering so the time between characters at the receiving end might not be the same as the time between characters at the sending end. The character format on the receiving side might be set different than the sending side so the parity and stop bits may be different.