  The formation of the red spirals is a puzzling issue in the standard picture
of galaxy formation and evolution. Most studies attribute the colour of the red
spirals to different environmental effects. We analyze a volume limited sample
from the SDSS to study the roles of small-scale and large-scale environments on
the colour of spiral galaxies. We compare the star formation rate, stellar age
and stellar mass distributions of the red and blue spirals and find
statistically significant differences between them at $99.9\%$ confidence
level. The red spirals inhabit significantly denser regions than the blue
spirals, explaining some of the observed differences in their physical
properties. However, the differences persist in all types of environments,
indicating that the local density alone is not sufficient to explain the origin
of the red spirals. Using an information theoretic framework, we find a small
but non-zero mutual information between the colour of spiral galaxies and their
large-scale environment that are statistically significant ($99.9\%$ confidence
level) throughout the entire length scale probed. Such correlations between the
colour and the large-scale environment of spiral galaxies may result from the
assembly bias. Thus both the local environment and the assembly bias may play
essential roles in forming the red spirals. The spiral galaxies may have
different assembly history across all types of environments. We propose a
picture where the differences in the assembly history may produce spiral
galaxies with different cold gas content. Such a difference would make some
spirals more susceptible to quenching. In all environments, the spirals with
high cold gas content could delay the quenching and maintain a blue colour,
whereas the spirals with low cold gas fractions would be easily quenched and
become red.
