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On 21 September 1996, a filament close to an area of enhanced network was observed with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer and Coronal Diagnostic Spectrometer (CDS). CDS provided intensity, Doppler shift and linewidth maps of the region in six lines whose temperature range covers 104 to 106 K. SUMER observations consisted of maps of the region in four hydrogen Lyman lines (Lδ, Lε, L-6, L-7) and a Svi line (944 Å). In all the Lyman lines we detect a central absorption and an asymmetry in the intensity of the two peaks. First NLTE computations indicate that such reversed Lyman profiles and their absolute intensities can be reproduced with the existing filament models provided that we take into account a prominence-corona transition region (PCTR). We discuss the Lyman lines' asymmetry in terms of macroscopic flows by comparison with the Hei line Doppler shifts observed with CDS.