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Heart rate variability results from the combined activity of several physiological systems, including the cardiac, vascular, and respiratory systems which have their own internal regulation, but also interact with each other to preserve the homeostatic function. These control mechanisms operate across multiple temporal scales, resulting in the simultaneous presence of short-term dynamics and long-range correlations. The Network Physiology framework provides statistical tools based on information theory able to quantify structural aspects of multivariate and multiscale interconnected mechanisms driving the dynamics of complex physiological networks. In this work, the multiscale representation of Transfer Entropy from Systolic Arterial Pressure (S) and Respiration (R) to Heart Period (H) and of its decomposition into unique, redundant and synergistic contributions is obtained using a Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This novel approach allows to quantify the directed information flow accounting for the simultaneous presence of short-term dynamics and long-range correlations among the analyzed processes. The approach is first illustrated in simulated VARFI processes and then applied to H, S and R time series measured in healthy subjects monitored at rest and during mental and postural stress. Our results highlight the dependence of the information transfer on the balance between short-term and long-range correlations in coupled dynamical systems, which cannot be observed using standard methods that do not consider long-range correlations. The proposed methodology shows that postural stress induces larger redundant effects at short time scales and mental stress induces larger cardiovascular information transfer at longer time scales.