Multiple approaches have been proposed to study differential splicing from RNA sequencing (RNA-seq) data, including the analysis of transcript isoforms, clusters of splice-junctions, alternative splicing events and exonic regions. However, many challenges remain unsolved, including the limitation in speed, the computing capacity and storage requirements, the constraints in the number of reads needed to achieve sufficient accuracy, and the lack of robust methods to account for variability between replicates and for analyses across multiple conditions. We present here a significant extension of SUPPA to enable streamlined analysis of differential splicing across multiple conditions, taking into account biological variability. We show that SUPPA differential splicing analysis achieves high accuracy using extensive experimental and simulated data compared to other methods; and shows higher accuracy at low sequencing depth, with short read lengths, and using replicas with unbalanced depth, which has important implications for the cost-effective use of RNA-seq data for splicing analysis. We also validate the analysis of multiple conditions with SUPPA by studying differential splicing during iPS-cell to neuron differentiation and during erythroblast differentiation, providing support for the applicability of SUPPA for the robust analysis of differential splicing beyond binary comparisons.