  We study intermediate--z SNe Ia using the empirical physical diagrams which
enable to learn about those SNe explosions. This information can be very useful
to reduce systematic uncertainties of the Hubble diagram of SNe Ia up to high
z. The study of the expansion velocities and the measurement of the ratio
$\mathcal{R}$(\SiII) allow to subtype those SNe Ia as done for nearby samples.
The evolution of this ratio as seen in the diagram $\mathcal{R}$(\SiII)--(t)
together with $\mathcal{R}$(\SiII)$_{max}$ versus (B-V)$_{0}$ indicate
consistency of the properties at intermediate z compared with local SNe. At
intermediate--z, the expansion velocities of Ca II and Si II are similar to the
nearby counterparts. This is found in a sample of 6 SNe Ia in the range
0.033$\leq z \leq$0.329 discovered within the {\it International Time
Programme} (ITP) of {\it Cosmology and Physics with SNe Ia} during the spring
of 2002. Those supernovae were identified using the 4.2m William Herschel
Telescope. Two SNe Ia at intermediate z were of the cool FAINT type, one being
a SN1986G--like object highly reddened. The $\mathcal{R}$(\SiII) ratio as well
as subclassification of the SNe Ia beyond templates help to place SNe Ia in
their sequence of brightness and to distinguish between reddened and
intrinsically red supernovae. This test can be done with very high z SNe Ia and
it will help to reduce systematic uncertainties due to extinction by dust. It
should allow to map the high-z sample into the nearby one.
