A multi-phase transport model is used to understand the origin of long-range collective azimuthal correlations in small-system collisions. To disentangle between collectivity associated with initialstate intrinsic momentum anisotropy and the collectivity arising as a final-state response to the collision geometry, we studied the development of collectivity in 5.02 TeV p+Pb collisions with both initial-state and final-state effects included. We find that the initial momentum anisotropy may not be fully isotropized through parton interactions, and the final-state partonic collectivity in general are correlated with both the initial momentum anisotropy and the shape of the collision geometry. The initial momentum anisotropy also influences the event by event fluctuation of collective flow. Therefore the mere evidence of geometry response of the collective flow can not rule out the presence of large contributions from the initial state.PACS numbers: 25.75. Gz, 25.75.Ld, In high-energy hadronic collisions, particle correlations are important tools to study the multi-parton dynamics of QCD in the strongly-coupled non-perturbative regime [1]. Measurements of azimuthal correlations have revealed a strong harmonic modulation of particle densi-where v n and Ψ n represent the magnitude and the phase of the n thorder harmonic, and are often denoted by flow vector V n = v n e inΨn [2]. The azimuthal correlations are found to be collective, involving many particles spread over a wide pseudorapidity range. Such azimuthal anisotropy was first observed in large A+A collision system [2-5], but are then observed and studied in small collision systems such as pp and p+Pb collisions at the LHC [6-13] and p+Au, d+Au and 3 He+Au collisions at RHIC [14][15][16][17][18][19].Although azimuthal anisotropy in A+A collisions is naturally explained as a result of hydrodynamic collective expansion of the hot and dense matter produced in the collision [20], the applicability of hydrodynamic picture for the azimuthal anisotropy in small collision systems such as pp or p+A collisions remains an open question [21][22][23]. It has been argued that the size is too small and life-time is too short for the matter in small system to hydrodynamize and approach local isotropization [24]. Instead, the azimuthal anisotropy may reflect intrinsic long-range momentum correlations of the dense gluon field right after the collision [25][26][27]. The current debate is focused on the timescale for the emergence of * jiangyong.jia@stonybrook.edu † glma@fudan.edu.cn collectivity: Is the collectivity born in the initial state, developed during non-equilibrium transport before the system hydrodynamizes, or arises even later when the system can be described by hydrodynamics? The latter two scenarios lead to a collectivity that correlates with the initial spatial eccentricities, while the first does not.The system produced right after the collision is highly anisotropic in momentum space, and the strong interactions among the constituents of the produce system tend to ...