  The Crab region was observed several times by INTEGRAL for calibration
purposes. This paper aims at underlining the systematic interactions between
(i) observations of this reference source, (ii) in-flight calibration of the
instrumental response and (iii) the development and validation of the analysis
tools of the SPI spectrometer. It first describes the way the response is
produced and how studies of the Crab spectrum lead to improvements and
corrections in the initial response. Then, we present the tools which were
developed to extract spectra from the SPI observation data and finally a Crab
spectrum obtained with one of these methods, to show the agreement with
previous experiments. We conclude with the work still ahead to understand
residual uncertainties in the response.
