Open Universe for blazars is a set of high-transparency data products for blazar science, and the tools designed to generate them. Blazar astrophysics is becoming increasingly data driven, depending on the integration and combined analysis of large quantities of data from the entire span of observational astrophysics techniques. The project was therefore chosen as one of the pilot activities within the United Nations Open Universe Initiative. In this work we developed a data analysis pipeline called Swift_deepsky, based on the Swift XRTDAS software and the XIMAGE package, encapsulated into a Docker container. Swift_deepsky, downloads and reads low-level data, generates higher-level products, detects X-ray sources and estimates several intensity and spectral parameters for each detection, thus facilitating the generation of complete and up-to-date science-ready catalogues from an entire space-mission dataset. The Docker version of the pipeline and its derived products is publicly available from the Open Universe Website at openuniverse.asi.it. We present the results of a detailed X-ray image analysis based on Swift_deepsky on all Swift XRT observations including a known blazar, carried out during the first 14 years of operations of the Swift Observatory. The resulting database includes over 27,000 images integrated in different X-ray bands, and a catalogue, called 1OUSXB, that provides intensity and spectral information for 33,396 X-ray sources, 8,896 of which are single or multiple detections of 2,308 distinct blazars. All the results can be accessed on-line in a variety of ways: e.g., from the Open Universe portal at openuniverse.asi.it, through Virtual Observatory services, via the VOU-Blazar tool and the SSDC SED builder. One of the most innovative aspects of this work is that the results can be safely reproduced and extended by anyone.