  We present the first experimental demonstration over a 43-km-long urban fiber
network of a local two-way optical frequency comparison, which does not require
any synchronization of the measurements. It was combined with a regular
active-noise compensation on another parallel fiber leading to a very reliable
and robust frequency transfer. This hybrid scheme enables us to investigate the
major limiting factors of the local two-way comparison. We analyze the
contribution to the phase noise of the recovered signal by the interferometers
at local and remote places. By using the ability of this set up to be injected
by a single laser or two independent lasers, we measure the contribution to the
long-term instability by the demodulated laser instabilities. We show that a
fractional frequency instability level of $1\times10^{-20}$ at 10 000 s can be
obtained with this simple setup after 43-km-long propagation in an urban area.
