Recent improvements in positioning technology has led to a much wider availability of massive moving object data. A crucial task is to find the moving objects that travel together. Usually, these object sets are called spatio-temporal patterns. Due to the emergence of many different kinds of spatio-temporal patterns in recent years, different approaches have been proposed to extract them. However, each approach only focuses on mining a specific kind of pattern. In addition to being a painstaking task due to the large number of algorithms used to mine and manage patterns, it is also time consuming. Moreover, we have to execute these algorithms again whenever new data are added to the existing database. To address these issues, we first redefine spatio-temporal patterns in the itemset context. Secondly, we propose a unifying approach, named GeT_Move, which uses a frequent closed itemset-based spatio-temporal pattern-mining algorithm to mine and manage different spatio-temporal patterns. GeT_Move is implemented in two versions which are GeT_Move and Incremental GeT_Move. To optimize the efficiency and to free the parameters setting, we also propose a Parameter Free Incremental GeT_Move algorithm. Comprehensive experiments are performed on real datasets as well as large synthetic datasets to demonstrate the effectiveness and efficiency of our approaches.