In 1994 Alcubierre developed the first warp drive theory using the original 3+1 ADM-MTW formalism. The original ADM-MTW formalism (Arnowitt-Dresner-Misner) (Misner-Thorne-Wheeler) uses both contravariant and covariant shift vector components in its mathematical structure.It possesses mixed shift vector components. Seven years later in 2001 the same original 3+1 ADM-MTW formalism appeared in the first part of the second warp driven theory developed by Natario.(The second part of Natario theory uses the Hodge Star). In this work we present two new 3+1 ADM-MTW formalisms: One is the parallel contravariant in which all the shift vector components in its mathematical structure are completely contravariant and the other one is the parallel covariant in which all the shift vector components in its mathematical structure are completely covariant. We describe both the original and symmetric Natario warp drive vectors using the mathematical techniques of these parallel formalisms. We focused ourselves in the 3D spherical coordinates for variable speeds. Remember that a real spaceship is a 3D object inserted inside a real 3D spacetime. Also a real warp drive must accelerate and de-accelerate. One the major drawbacks concerning warp drives is the problem of the Horizons(causally disconnected portions of spacetime) in which an observer in the center of the bubble cannot signal nor control the front part of the bubble. The behavior of a photon sent to the front of the warp bubble in the case of the original and symmetric Natario warp drive vectors with variable speeds and a lapse function was also one of the main purposes of this work. We presented the behavior of a photon sent to the front of the bubble in the original and symmetric Natario warp drive vectors with the lapse function in these new parallel 3+1 ADM-MTW formalisms using quadratic forms and the null-like geodesics $ds^2=0$ of General Relativity and we provided here the step by step mathematical calculations in order to outline the final results found in our work which are the following ones: For the case of the lapse function or the 3+1 spacetime in these parallel ADM-MTW formalisms the Horizon do not exists at all. Due to the extra terms in the lapse function or the presence of the 3D dimensions that affects the whole spacetime geometry these solutions allows to circumvent the problem of the Horizon.