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.
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