The present invention is a cell cultivating vessel or device, such as a single or multitier flask, including a cover having a top plate, a side wall and a resealable port; an intermediate tray for receiving cells and cell culture media, having a bottom plate, a side wall, and a gap region formed between an interior upwardly angled lip located on an interior portion of the intermediate tray bottom plate and an adjacent outwardly angled side wall portion of the intermediate tray bottom plate, wherein the lip has a outwardly swooping curvilinear edge feature; and a base tray for receiving the cells and cell culture media, including a bottom plate and a side wall. The intermediate tray is positioned between the cover and the base tray, such that the gap region of the intermediate tray bottom plate is in alignment with the port located on the cover, resulting in the port, the intermediate tray and the base tray in fluid communication with one another which provides direct access, such as by a user to remove and/or add cells, cell media, and nutrients located on each of the intermediate and/or the base trays. Alternatively, the cell cultivating flask includes a plurality of intermediate trays stacked on top of one another and the gap regions of each intermediate tray are in alignment with each other and with the port on the cover.