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The LABEC laboratory, the INFN ion beam laboratory of nuclear techniques for environment and cultural heritage, located in the Scientific and Technological Campus of the University of Florence in Sesto Fiorentino, started its operational activities in 2004, after INFN decided in 2001 to provide our applied nuclear physics group with a large laboratory dedicated to applications of accelerator-related analytical techniques, based on a new 3 MV Tandetron accelerator. The new accelerator greatly improved the performance of existing Ion Beam Analysis (IBA) applications (for which we were using since the 1980s an old single-ended Van de Graaff accelerator) and in addition allowed to start a novel activity of Accelerator Mass Spectrometry (AMS), in particular for 14C dating. Switching between IBA and AMS operation became very easy and fast, which allowed us high flexibility in programming the activities, mainly focused on studies of cultural heritage and atmospheric aerosol composition, but including also applications to biology, geology, material science and forensics, ion implantation, tests of radiation damage to components, detector performance tests and low-energy nuclear physics. This paper describes the facilities presently available in the LABEC laboratory, their technical features and some success stories of recent applications.