Capture-recapture (CR) models are an essential tool for estimating demographic parameters in most animal and some plant populations. To avoid drawing incorrect conclusions in any statistical inference, a crucial prerequisite is to assess the goodness of fit of a general model to the data. In CR models, a frequent cause of lack of fit, is the so-called transience effect, which is due to a lower expectation of re-observation of individuals marked for the first time as compared to other individuals. The transience effect may result either from different biological causes or from the sampling procedure. A transience effect is usually treated by distinguishing at least two age-classes in the survival probability, but other approaches may be more suitable. Here we develop a conceptual and analytical framework for including a transience effect in capture-recapture models. We show the implementation of two additional parametrizations that incorporate a transience effect. With these parametrizations, we can directly estimate the "transience probability" defined as the probability that a newly caught individual disappear from the population beyond what is expected based on the behavior of the previously caught individuals in the same sample. Additionally, these parametrizations allow testing biological hypotheses concerning drivers affecting this probability. Results from our case study show differences between parametrizations, with the parametrization most currently used giving different estimates, especially when including covariates. We advocate for a unifying framework for treating a transience effect, that helps clarifying the ideas and terminology, and where the biological reasons should be the rule for choosing the appropriate analytical procedure. This framework will also open new and powerful ways for the detection and exploration of ecological processes such as the costs of the first reproduction or the deleterious effects of some types of marking.