State Space Models (SSMs) have recently enjoyed a rise to prominence in the field of deep learning for sequence modeling, especially as an alternative to Transformers. Their success stems from avoiding two well-known drawbacks of attention-based models: quadratic complexity with respect to the sequence length and inability to model long-range dependencies. The SSM variant Mamba has demonstrated performance comparable to Transformers without any form of attention, thanks to the use of a selective mechanism for the state parameters. Selectivity, however, is only evaluated empirically and the reasons of its effectiveness remain unclear. In this work, we show how selectivity is related to the sequence processing. Our analysis shows that selective time intervals in Mamba act as linear approximators of information. Then, we propose our SeRpEnt architecture, a SSM that further exploits selectivity to compress sequences in an information-aware fashion. It employs a resampling mechanism that aggregates elements based on their information content. Our empirical results in the Long Range Arena benchmark and other language modeling tasks show benefits of the SeRpEnt's resampling mechanism.