  The X-ray transient MXB 0656-072 is a poorly studied member of high-mass
X-ray binaries. Based on the transient nature of the X-ray emission, the
detection of pulsations, and the early-type companion, it has been classified
as a Be X-ray binary (Be/XRB). However, the flaring activity covering a large
fraction of a giant outburst is somehow peculiar. Our goal is to investigate
the multiwavelength variability of the high-mass X-ray binary MXB 0656-072. We
carried out optical spectroscopy and analysed all RXTE archive data, performing
a detailed X-ray-colour, spectral, and timing analysis of both normal (type-I)
and giant (type-II) outbursts from MXB 0656-072 This is the first detailed
analysis of the optical counterpart in the classification region (4000-5000 A).
From the strength and ratio of the elements and ions, we derive an O9.5Ve
spectral type, in agreement with previous classification. This confirms its Be
nature. The characterisation of the Be/XRB system relies on Balmer lines in
emission in the optical spectra, long-term X-ray variability, and the orbital
period vs. spin period and EW(H\alpha) relation. The peculiar feature that
distinguishes the type-II outburst is flaring activity, which occurs during the
whole outburst peak, before a smoother decay. We interpret it in terms of
magneto-hydrodynamic instability. Colour and spectral analysis reveal a
hardening of the spectrum as the flux increases. We explored the aperiodic
X-ray variability of the system for the first time, finding a correlation of
the central frequency and rms of the main timing component with luminosity,
which extends up to a "saturation" flux of 1E-8 erg/cm^2/s. A correlation
between timing and spectral parameters was also found, pointing to an
interconnection between the two physical regions responsible for both
phenomenologies.
