The cortex processes information through distributed networks of functionally heterogeneous brain areas. This processing requires spiking activity to be transferred between these different areas while preserving the information it carries. Using numerical simulations, we can study how the connectivity determines the transfer of spiking activity (what can be transferred and how) and what traces will be left in the cortex at the level of the connectivity by the need to transfer certain spiking features. In the first part of the talk, I will discuss the propagation of spiking activity in strongly diluted feedforward networks. I will show that in these architectures, oscillatory activity can propagate by exploiting the resonance properties of recurrent networks of excitatory and inhibitory neurons. In the second part of the talk, I will discuss how input correlations can modulate the transfer of spiking activity features such as firing rates and inter-spike interval regularity and what may be the implications for the connectivity in the cortex. Based on these observations, I will propose a feedforward model that successfully captures the modulation of spiking features that is typically observed during evoked responses and in relation with attention in the cortex.