  Using molecular dynamic simulations we study three families of continuous
core-softened potentials consisting of two length scales: a shoulder scale and
an attractive scale. All the families have the same slope between the two
length scales but exhibit different potential energy gap between them. For each
family three shoulder depths are analyzed. We show that all these systems
exhibit a liquid-liquid phase transition between a high density liquid phase
and a low density liquid phase ending at a critical point. The critical
temperature is the same for all cases suggesting that the critical temperature
is only dependent on the slope between the two scales. The critical pressure
decreases with the decrease of the potential energy gap between the two scales
suggesting that the pressure is responsible for forming the high density
liquid. We also show, using the radial distribution function and the excess
entropy analysis, that the density, the diffusion and the structural anomalies
are present if particles move from the attractive scale to the shoulder scale
with the increase of the temperature indicating that the anomalous behavior
depends only in what happens up to the second coordination shell.
