Sequence in rolling, adhesion, and emigration of Leukocytes:

After WBC gets at peripheral site, chemical mediators released during  inflammatory process acts on endothelial cell and activate them.

After activation of endothelial cell by cytokines and other mediators produced locally, endothelial cells express adhesin molecule called Weilbel-Palade bodies.(locally produced mediators)

Leukocytes attach loosely to these molecules. These cells bind and detach and begins to tumble on endothelial surface. This process is called rolling.

After cytokines acts on endothelial cells, selectins molecules are expressed on both leukocytes and endothelium and rolling of leukocytes mediates. Rolling leukocytes then sense changes in endothelium which initiate adhesion of leukocyte to endothelial surface.

After rolling leukocytes gets activated by chemokines displayed on endothelial surface, their integrins undergoes conformational change and cluster together, converting to high-affinity form. At same time, other cytokines TNF and IL-1 activates endothelial cells to increase their expression of ligands for integrins. These ligands are ICAM-1 which bind to integrins LFA-1 (leukocyte-function associated antigen) and MAC-1 (macrophage-1 antigen) and VCAM-1 which binds to integrins VLA-4 (Very late antigen 4).

Binding to ICAM and VCAM is strong bond and WBC adhesion occurs. This is due to cytoskeletal changes in leukocytes which mediate firm attachment to substrate.

After being arrested on endothelial surface, leukocyte migrate through vessel wall by squeezing between inter-endothelial junctions. This is mediated by PECAM (Platelet Endothelial Cell Adhesion Molecule).

Leukocytes after resting on basement membrane secretes collagenases. 

Collagenases digest collagen present on basement membrane of endothelial cell.

As a result, there is formation of hole on basement membrane from which leukocytes pass through vascular basement membrane.